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Index: By Contributors. Thank you!

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• bookofproofs (8396)
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  • Algorithm: Addition (or Subtraction) of Two Registers
  • Algorithm: Assignment of a Constant `\(c\)` to the Register `\(r_i\)` with a `\(L O O P\)`-Program
  • Algorithm: Calculation of Inverses Modulo a Number (Python)
  • Algorithm: Complex Numbers
  • Algorithm: Conditional execution of `\(L O O P\)` programs - IF-THEN construct
  • Algorithm: Conditional execution of `\(L O O P\)` programs - IF-THEN-ELSE construct
  • Algorithm: Continued Fraction (Python)
  • Algorithm: Converting Decimal Numbers to Roman Numbers
  • Algorithm: Converting Roman Numbers to Decimal Numbers
  • Algorithm: Division with Quotient and Remainder (Unit-cost Random Access Machine)
  • Algorithm: Extended Greatest Common Divisor (Python)
  • Algorithm: Get All Components of a Graph
  • Algorithm: Get the Component Induced by Vertices Connected to a Given Vertex
  • Algorithm: Get the Cut Vertices and Biconnected Components of a Connected Graph
  • Algorithm: Graph (Python)
  • Algorithm: Greatest Common Divisor (Python)
  • Algorithm: Horner Scheme
  • Algorithm: Jacobi Symbol (Python)
  • Algorithm: Multiplication of Two Registers
  • Algorithm: No-Operation Command (NOP)
  • Algorithm: Sequential Search
  • Algorithm: Setting the value of a register to the value of another register plus or minus a constant
  • Algorithm: getSubgraph
  • Application: Application of Monotonic Convergence (related to Theorem: Every Bounded Monotonic Sequence Is Convergent)
  • Application: Application of the Rabin-Scott Theorem - the Rabin-Scott Algorithm (related to Chapter: Finite Automata (Finite Sequential Machines))
  • Application: Application of the Theorem to Reduce `$\epsilon$`-NFA to NFA (related to Chapter: Finite Automata (Finite Sequential Machines))
  • Application: Lightning and Thunder or the Relativity of Acoustic Signals (related to Part: Oddities and Curiosities)
  • Application: SLEs Revised in the Light of Vector Spaces (related to Chapter: Vectors Revised - Vector Spaces)
  • Axiom: "Between" Relation, Axioms of Order
  • Axiom: 1.1: Straight Line Determined by Two Distinct Points
  • Axiom: 1.2: Segment Extension
  • Axiom: 1.3: Circle Determined by its Center and its Radius
  • Axiom: 1.4: Equality of all Right Angles
  • Axiom: 1.5: Parallel Postulate
  • Axiom: Addition of the Probability of Mutually Exclusive Events
  • Axiom: Archimedean Axiom
  • Axiom: Axiom of Choice
  • Axiom: Axiom of Distributivity
  • Axiom: Axiom of Empty Set
  • Axiom: Axiom of Existence
  • Axiom: Axiom of Extensionality
  • Axiom: Axiom of Foundation
  • Axiom: Axiom of Infinity
  • Axiom: Axiom of Pairing
  • Axiom: Axiom of Power Set
  • Axiom: Axiom of Replacement (Schema)
  • Axiom: Axiom of Union
  • Axiom: Axioms of Connection
  • Axiom: Axioms of Group
  • Axiom: Axioms of Magma
  • Axiom: Axioms of Monoid
  • Axiom: Axioms of Semigroup
  • Axiom: Bivalence of Truth
  • Axiom: Filter
  • Axiom: Peano Axioms
  • Axiom: Principle of Relativity
  • Axiom: Principle of the Constancy of Light Speed
  • Axiom: Probability as a Non-Negative Number
  • Axiom: Probability of the Certain Event
  • Axiom: Schema of Separation Axioms (Restricted Principle of Comprehension)
  • Axiom: Separation Axioms
  • Axiom: Zermelo-Fraenkel Axioms
  • Branch: Algebra
  • Branch: Analysis
  • Branch: Combinatorics and Discrete Mathematics
  • Branch: Game Theory
  • Branch: Geometry
  • Branch: Graph Theory
  • Branch: Introduction to the Axiomatic Method
  • Branch: Knot Theory
  • Branch: Logic
  • Branch: Number Systems and Arithmetics
  • Branch: Number Theory
  • Branch: Probability Theory and Statistics
  • Branch: Riddles, Puzzles and Brain-Teasers
  • Branch: Set Theory
  • Branch: Theoretical Computer Science
  • Branch: Theoretical Physics
  • Branch: Topology
  • Chapter: Abel Integral Equations
  • Chapter: Affine Spaces
  • Chapter: Algebraic Properties of Complex Numbers
  • Chapter: Algebraic and Transcendent Numbers
  • Chapter: An Introduction to the Principle of Duality in Projective Geometry
  • Chapter: And / Or Trees
  • Chapter: Applications of the Fundamental Theorem of the Difference Calculus
  • Chapter: Arithmetic Functions
  • Chapter: Arithmetical and Algebraic Problems
  • Chapter: Around 1600 - The homogeneity principle and the birth of the mathematical formula
  • Chapter: Avoidance of Negative Solutions, Descartes' Analysis and Synthesis
  • Chapter: Banach Spaces and Banach Algebra
  • Chapter: Basic Geometric Concepts in Projective Geometry
  • Chapter: Basic Topological Concepts
  • Chapter: Basics of Real Analysis of One Variable
  • Chapter: Binary Relations and Their Properties
  • Chapter: Bipartite Graphs
  • Chapter: Branch and Bound
  • Chapter: Calculation of Roots
  • Chapter: Calendar
  • Chapter: Can Cardinals be Ordered?
  • Chapter: Chebyshev's Lemma
  • Chapter: Chessboard Problems
  • Chapter: Classification of Differential Equations
  • Chapter: Classification of Formal Languages
  • Chapter: Classifying the Logical Calculi - Variables, Formulas, Predicates and Signatures
  • Chapter: Colorings of Planar Graphs
  • Chapter: Combination and Group Problems
  • Chapter: Combinatorial Algorithms
  • Chapter: Compact Sets
  • Chapter: Completeness of Real Numbers
  • Chapter: Conditions for Planarity and Planarity Testing
  • Chapter: Congruence Classes and Modular Arithmetic
  • Chapter: Construction of Topologies
  • Chapter: Continuity
  • Chapter: Continuous Time Markov Chains
  • Chapter: Continuum Hypothesis
  • Chapter: Contraction and Minors
  • Chapter: Contradictory Propositions in Propositional Logic
  • Chapter: Correctness
  • Chapter: Criteria for Convergence of Sequences
  • Chapter: Crossing River Problems
  • Chapter: Cryptography
  • Chapter: Data Compression
  • Chapter: Decidability
  • Chapter: Density and Countability
  • Chapter: Determinants
  • Chapter: Differentiability
  • Chapter: Differential Operations on Vector Fields
  • Chapter: Differentiation
  • Chapter: Digraphs
  • Chapter: Discrete Fourier Transform (DFT)
  • Chapter: Discrete Time Markov Chains
  • Chapter: Divisibility
  • Chapter: Divisibility and Modular Arithmetic
  • Chapter: Divisibility in General Rings
  • Chapter: Dynamic Programming
  • Chapter: Eigenvalues and Eigenvectors
  • Chapter: Eigenvalues and Eigenvectors
  • Chapter: Elementary Results About Prime Numbers
  • Chapter: Entropy
  • Chapter: Equivalent Transformations in Propositional Logic
  • Chapter: Error Analysis
  • Chapter: Euclid's “Elements”
  • Chapter: External Sorting
  • Chapter: Extrapolation
  • Chapter: Fields (Overview)
  • Chapter: Files
  • Chapter: Finite Automata (Finite Sequential Machines)
  • Chapter: Fisher Distribution
  • Chapter: Fixed Point Theory
  • Chapter: Fourier Series
  • Chapter: Fractional Arithmetic
  • Chapter: Fredholm Integral Equations
  • Chapter: From the Syntax to the Semantics of Formal Languages
  • Chapter: Functions (Maps)
  • Chapter: Fuzzy Logic
  • Chapter: Genetic Programming
  • Chapter: Geometric Aspects
  • Chapter: Geometrical Problems
  • Chapter: Goldbach Conjecture
  • Chapter: Graph Representations
  • Chapter: Graph-Theoretic Algorithms
  • Chapter: Graphs
  • Chapter: Graphs
  • Chapter: Greedy Algorithms
  • Chapter: Group-theoretic Problems
  • Chapter: Groups (Overview)
  • Chapter: Hashing
  • Chapter: Hilbert Spaces
  • Chapter: Hilbert's Axiomatic System
  • Chapter: Hypergeometric Distribution
  • Chapter: Important Properties of Binary Operations
  • Chapter: Infinite Products - Overview
  • Chapter: Infinite Series - Overview
  • Chapter: Infinite Series Approximations
  • Chapter: Integrability
  • Chapter: Integral Operations on Vector Fields
  • Chapter: Integration
  • Chapter: Integration of Starting Value Problems (Ordinary DE)
  • Chapter: Interpolation
  • Chapter: Introduction to Matrices and Vectors
  • Chapter: Invalid Logical Arguments
  • Chapter: Isolated Singularities
  • Chapter: Isomorphism (Graphs)
  • Chapter: Jordan Normal Form
  • Chapter: Laplace Probability
  • Chapter: Laurant Series
  • Chapter: Lebesgue Measure and Lebesgue Integral
  • Chapter: Linear Equation Systems
  • Chapter: Linear Equations and Systems of Linear Equations (SLEs)
  • Chapter: Linear Operators and Linear Functionals
  • Chapter: Linear Programming
  • Chapter: Linked Lists
  • Chapter: Liouville-Neumann Series
  • Chapter: Logarithmic Normal Distribution
  • Chapter: Logical Arguments Used in Mathematical Proofs
  • Chapter: Magic Square Problems
  • Chapter: Magmas, Semigroups, Monoids (Overview)
  • Chapter: Mazes and How to Thread Them
  • Chapter: Measuring, Weighing, and Packing Problems
  • Chapter: Meromorphic Functions
  • Chapter: Methods to Solve Ordinary DE
  • Chapter: Methods to Solve Partial DE
  • Chapter: Min-Max and Alpha-Beta
  • Chapter: Mixing
  • Chapter: Models of Computation
  • Chapter: Modules (Overview)
  • Chapter: Moving Counter Problems
  • Chapter: Multiplication
  • Chapter: Network Flows
  • Chapter: Network Paths
  • Chapter: Neural Networks
  • Chapter: Non-Linear Equation Systems
  • Chapter: Non-linear Operator
  • Chapter: Normal Distribution
  • Chapter: Normal Forms in `$PL0$`
  • Chapter: Order
  • Chapter: Order Relations
  • Chapter: Orthogonalisation
  • Chapter: Peano Arithmetic
  • Chapter: Points and Lines Problems
  • Chapter: Poisson Distribution
  • Chapter: Polynomial Rings, Irreducibility, and Field Extensions
  • Chapter: Positional Notation Systems
  • Chapter: Power Series Introduction
  • Chapter: Preface
  • Chapter: Prime Number Theorem
  • Chapter: Prime Number Theorem for Arithmetic Progressions
  • Chapter: Principal Axis Transformation
  • Chapter: Problems Concerning Games
  • Chapter: Product Manipulation Methods
  • Chapter: Properties of Complex Functions
  • Chapter: Properties of Real Functions
  • Chapter: Pseudo-Random Numbers
  • Chapter: Putting it All Together - Syntax and Semantics of a Logical Calculus
  • Chapter: Puzzle Games
  • Chapter: Quadratic Residues
  • Chapter: Quantum Computation
  • Chapter: Queues
  • Chapter: Random Sample Models
  • Chapter: Randomized Rounding
  • Chapter: Real Numbers As Limits Of Rational Numbers
  • Chapter: Real-valued Sequences and Limits of Sequences and Functions
  • Chapter: Reduction
  • Chapter: Renaissance and Beginnings of the Infinitesimal Methods
  • Chapter: Representation of Functions as Taylor Series
  • Chapter: Residue Theorem
  • Chapter: Rings (Overview)
  • Chapter: Roman Numbers
  • Chapter: Rotations and Basic Transformations
  • Chapter: Satisfaction Problem Solving
  • Chapter: Searching
  • Chapter: Sequences and Limits
  • Chapter: Sequences of Numbers
  • Chapter: Set Operations
  • Chapter: Sets
  • Chapter: Sieve Methods
  • Chapter: Similarity of Graphs
  • Chapter: Simple Connectivity
  • Chapter: Simple Facts Regarding Cardinals
  • Chapter: Simple Formulas Involving the Complex Numbers
  • Chapter: Simulated Annealing
  • Chapter: Solving Diophantine Equations
  • Chapter: Some Important Constants
  • Chapter: Sorting
  • Chapter: Stacks
  • Chapter: String Matching
  • Chapter: Strings
  • Chapter: Strong Law of Large Numbers
  • Chapter: Student Distribution
  • Chapter: Sum Manipulation Methods
  • Chapter: Symmetry Groups
  • Chapter: The Paradox Party
  • Chapter: The Proving Machine - an Automation of Logical Reasoning
  • Chapter: The `$C(X)$` Algebra
  • Chapter: The `$\chi^2$` Distribution
  • Chapter: Topological Aspects
  • Chapter: Trees
  • Chapter: Triangle of the Stirling Numbers of the First Kind
  • Chapter: Triangle of the Stirling Numbers of the Second Kind
  • Chapter: Types of Complex Functions
  • Chapter: Types of Real Functions
  • Chapter: Unclassified Problems
  • Chapter: Unicursal and Route Problems
  • Chapter: Uniform Distribution
  • Chapter: Useful Inequalities
  • Chapter: Vector Properties of Complex Numbers
  • Chapter: Vector Spaces (Overview)
  • Chapter: Vectors
  • Chapter: Vectors Revised - Vector Spaces
  • Chapter: Volterra Integral Equation
  • Chapter: Weak Law of Large Numbers
  • Chapter: Zeta Functions
  • Corollary: (Real) Exponential Function Is Always Positive (related to Corollary: Reciprocity of Exponential Function, Non-Zero Property)
  • Corollary: 11.35: Condition for Equal Angles contained by Elevated Straight Lines from Plane Angles (related to Proposition: Prop. 11.35: Condition for Equal Angles contained by Elevated Straight Lines from Plane Angles)
  • Corollary: 3.01: Bisected Chord of a Circle Passes the Center (related to Proposition: 3.01: Finding the Center of a given Circle)
  • Corollary: 3.16: Line at Right Angles to Diameter of Circle At its Ends Touches the Circle (related to Proposition: 3.16: Line at Right Angles to Diameter of Circle At its Ends Touches the Circle)
  • Corollary: 4.15: Side of Hexagon Inscribed in a Circle Equals the Radius of that Circle (related to Proposition: 4.15: Side of Hexagon Inscribed in a Circle Equals the Radius of that Circle)
  • Corollary: 5.07: Ratios of Equal Magnitudes (related to Proposition: 5.07: Ratios of Equal Magnitudes)
  • Corollary: 5.19: Proportional Magnitudes have Proportional Remainders (related to Proposition: 5.19: Proportional Magnitudes have Proportional Remainders)
  • Corollary: 6.08: Geometric Mean Theorem (related to Proposition: 6.08: Perpendicular in Right-Angled Triangle makes two Similar Triangles)
  • Corollary: 6.19: Ratio of Areas of Similar Triangles (related to Proposition: 6.19: Ratio of Areas of Similar Triangles)
  • Corollary: 6.20: Similar Polygons are Composed of Similar Triangles (related to Proposition: 6.20: Similar Polygons are Composed of Similar Triangles)
  • Corollary: 7.02: Any Divisor Dividing Two Numbers Divides Their Greatest Common Divisor (related to Proposition: 7.02: Greatest Common Divisor of Two Numbers - Euclidean Algorithm)
  • Corollary: 8.02: Construction of Geometric Progression in Lowest Terms (related to Proposition: 8.02: Construction of Geometric Progression in Lowest Terms)
  • Corollary: 9.11: Elements of Geometric Progression from One which Divide Later Elements (related to Proposition: Prop. 9.11: Elements of Geometric Progression from One which Divide Later Elements)
  • Corollary: A Criterion for Isosceles Triangles (related to Proposition: 1.06: Isosceles Triagles II)
  • Corollary: A product of two real numbers is zero if and only if at least one of these numbers is zero. (related to Corollary: `\(0x=0\)`)
  • Corollary: Abelian Group of Vectors Under Addition (related to Proposition: Abelian Group of Matrices Under Addition)
  • Corollary: Algebraic Structure of Strings over an Alphabet (related to Definition: Strings (words) over an Alphabet)
  • Corollary: All Boolean Functions Can Be Built Using Conjunction, Disjunction, and Negation (related to Lemma: Construction of Conjunctive and Disjunctive Canonical Normal Forms)
  • Corollary: All Uniformly Continuous Functions are Continuous (related to Definition: Uniformly Continuous Functions (Real Case))
  • Corollary: All Zeros of Cosine and Sine (related to Proposition: Special Values for Real Sine, Real Cosine and Complex Exponential Function)
  • Corollary: Angles and Sides in a Triangle V (related to Proposition: 1.25: Angles and Sides in a Triangle IV)
  • Corollary: Angles of Right Triangle (related to Proposition: 1.32: Sum Of Angles in a Triangle and Exterior Angle)
  • Corollary: Angles of a Right And Isosceles Triangle (related to Proposition: 1.32: Sum Of Angles in a Triangle and Exterior Angle)
  • Corollary: Arguments for which Cosine and Sine are Equal to Each Other (related to Proposition: Special Values for Real Sine, Real Cosine and Complex Exponential Function)
  • Corollary: Barycentric Coordinates, Barycenter (related to Definition: Affine Basis, Affine Coordinate System)
  • Corollary: Bisectors of Two Supplemental Angles Are Right Angle To Each Other (related to Proposition: 1.13: Angles at Intersections of Straight Lines)
  • Corollary: Bounds for the Minimal Tree Decomposability (related to Definition: Minimal Tree Decomposability)
  • Corollary: Cartesian Products of Countable Sets Is Countable (related to Proposition: Union of Countably Many Countable Sets)
  • Corollary: Circular References Of Self-Contained Sets Are Forbidden (related to Axiom: Axiom of Foundation)
  • Corollary: Closed Real Intervals Are Compact (related to Proposition: Closed n-Dimensional Cuboids Are Compact)
  • Corollary: Commutativity of Conjunction (related to Definition: Conjunction)
  • Corollary: Commutativity of Disjunction (related to Definition: Disjunction)
  • Corollary: Commutativity of Equivalence (related to Definition: Equivalence)
  • Corollary: Continuous Functions Mapping Compact Domains to Real Numbers are Bounded (related to Theorem: Continuous Functions Mapping Compact Domains to Real Numbers Take Maximum and Minimum Values on these Domains)
  • Corollary: Continuous Real Functions on Closed Intervals are Bounded (related to Proposition: Continuous Real Functions on Closed Intervals Take Maximum and Minimum Values within these Intervals)
  • Corollary: Contraposition of Cancellative Law for Adding Natural Numbers (related to Proposition: Addition of Natural Numbers Is Cancellative)
  • Corollary: Convergence of Complex Conjugate Sequence (related to Proposition: Convergent Complex Sequences Vs. Convergent Real Sequences)
  • Corollary: Cor. 10.003: Greatest Common Measure of Commensurable Magnitudes (related to Proposition: Prop. 10.003: Greatest Common Measure of Commensurable Magnitudes)
  • Corollary: Cor. 10.004: Greatest Common Measure of Three Commensurable Magnitudes (related to Proposition: Prop. 10.004: Greatest Common Measure of Three Commensurable Magnitudes)
  • Corollary: Cor. 10.006: Magnitudes with Rational Ratio are Commensurable (related to Proposition: Prop. 10.006: Magnitudes with Rational Ratio are Commensurable)
  • Corollary: Cor. 10.009: Commensurability of Squares (related to Proposition: Prop. 10.009: Commensurability of Squares)
  • Corollary: Cor. 10.023: Segment Commensurable with Medial Area is Medial (related to Proposition: Prop. 10.023: Segment Commensurable with Medial Segment is Medial)
  • Corollary: Cor. 10.111: Thirteen Irrational Straight Lines of Different Order (related to Proposition: Prop. 10.111: Apotome not same with Binomial Straight Line)
  • Corollary: Cor. 10.114: Rectangles With Irrational Sides Can Have Rational Areas (related to Proposition: Prop. 10.114: Area contained by Apotome and Binomial Straight Line Commensurable with Terms of Apotome and in same Ratio)
  • Corollary: Cor. 11.33: Volumes of Similar Parallelepipeds are in Triplicate Ratio to Length of Corresponding Sides (related to Proposition: Prop. 11.33: Volumes of Similar Parallelepipeds are in Triplicate Ratio to Length of Corresponding Sides)
  • Corollary: Cor. 12.07: Prism on Triangular Base divided into Three Equal Tetrahedra (related to Proposition: Prop. 12.07: Prism on Triangular Base divided into Three Equal Tetrahedra)
  • Corollary: Cor. 12.08: Volumes of Similar Tetrahedra are in Cubed Ratio of Corresponding Sides (related to Proposition: Prop. 12.08: Volumes of Similar Tetrahedra are in Cubed Ratio of Corresponding Sides)
  • Corollary: Cor. 12.17: Construction of Polyhedron in Outer of Concentric Spheres (related to Proposition: Prop. 12.17: Construction of Polyhedron in Outer of Concentric Spheres)
  • Corollary: Cor. 13.16: Construction of Regular Icosahedron within Given Sphere (related to Proposition: Prop. 13.16: Construction of Regular Icosahedron within Given Sphere)
  • Corollary: Cor. 13.17: Construction of Regular Dodecahedron within Given Sphere (related to Proposition: Prop. 13.17: Construction of Regular Dodecahedron within Given Sphere)
  • Corollary: Cosine and Sine are Periodic Functions (related to Proposition: Special Values for Real Sine, Real Cosine and Complex Exponential Function)
  • Corollary: Derivative of a Constant Function (related to Definition: Constant Function Real Case)
  • Corollary: Derivative of a Linear Function `\(ax+b\)` (related to Definition: Linear Function)
  • Corollary: Diagonals of a Rectangle (related to Proposition: 1.34: Opposite Sides and Opposite Angles of Parallelograms)
  • Corollary: Diagonals of a Rhombus (related to Proposition: 1.34: Opposite Sides and Opposite Angles of Parallelograms)
  • Corollary: Differentiable Functions are Continuous (related to Proposition: Differentiable Functions and Tangent-Linear Approximation)
  • Corollary: Diophantine Equations of Congruences Have a Finite Number Of Solutions (related to Proposition: Diophantine Equations of Congruences)
  • Corollary: Divisors of a Product Of Many Factors, Co-Prime to All But One Factor, Divide This Factor (related to Proposition: Divisors of a Product Of Two Factors, Co-Prime to One Factor Divide the Other Factor)
  • Corollary: Equality of Sets (related to Axiom: Schema of Separation Axioms (Restricted Principle of Comprehension))
  • Corollary: Equivalent Statements Regarding Parallel Lines (related to Proposition: 1.29: Parallel Lines III)
  • Corollary: Estimating the Growth of a Function with its Derivative (related to Theorem: Darboux's Theorem)
  • Corollary: Even Number of Vertices with an Odd Degree in Finite Digraphs (related to Lemma: Handshaking Lemma for Finite Digraphs)
  • Corollary: Even Number of Vertices with an Odd Degree in Finite Graphs (related to Lemma: Handshaking Lemma for Finite Graphs)
  • Corollary: Every Distance Is Positive Definite (related to Definition: Metric (Distance))
  • Corollary: Every Equilateral Triangle Is Equiangular. (related to Proposition: 1.05: Isosceles Triangles I)
  • Corollary: Every uniformly convergent sequence of functions is pointwise convergent. (related to Definition: Pointwise and Uniform Convergence)
  • Corollary: Exchanging the Limit of Function Values with the Function Value of the Limit of Arguments (related to Definition: Continuous Functions at Single Real Numbers)
  • Corollary: Existence of Arbitrarily Small Positive Rational Numbers (related to Axiom: Archimedean Axiom)
  • Corollary: Existence of Arbitrarily Small Powers (related to Axiom: Archimedean Axiom)
  • Corollary: Existence of Natural Numbers Exceeding Positive Real Numbers (Archimedian Principle) (related to Axiom: Archimedean Axiom)
  • Corollary: Existence of Natural One (Neutral Element of Multiplication of Natural Numbers) (related to Definition: Multiplication of Natural Numbers)
  • Corollary: Existence of Natural Zero (Neutral Element of Addition of Natural Numbers) (related to Proposition: Addition Of Natural Numbers)
  • Corollary: Existence of Parallel Straight Lines (related to Proposition: 1.16: The Exterior Angle Is Greater Than Either of the Non-Adjacent Interior Angles)
  • Corollary: Existence of Powers Exceeding Any Positive Constant (related to Axiom: Archimedean Axiom)
  • Corollary: Existence of Unique Integers Exceeding Real Numbers (related to Axiom: Archimedean Axiom)
  • Corollary: Exponential Function Is Non-Negative (Real Case) (related to Proposition: Functional Equation of the Exponential Function)
  • Corollary: Exponential Function Is Strictly Monotonically Increasing (related to Proposition: Functional Equation of the Exponential Function)
  • Corollary: Exponential Function and the Euler Constant (related to Proposition: Functional Equation of the Exponential Function)
  • Corollary: Functions Continuous at a Point and Identical to Other Functions in a Neighborhood of This Point (related to Definition: Continuous Functions at Single Real Numbers)
  • Corollary: General Associative Law (related to Definition: Associativity)
  • Corollary: General Associative Law of Multiplication (related to Proposition: Multiplication of Real Numbers Is Associative)
  • Corollary: General Commutative Law (related to Definition: Commutativity)
  • Corollary: General Commutative Law of Multiplication (related to Proposition: Multiplication of Real Numbers Is Commutative)
  • Corollary: Intersection of Convex Affine Sets (related to Definition: Convex Affine Set)
  • Corollary: Irrational Numbers are Uncountable (related to Proposition: Real Numbers are Uncountable)
  • Corollary: Justification of Power Set (related to Axiom: Axiom of Power Set)
  • Corollary: Justification of Set Intersection (related to Axiom: Schema of Separation Axioms (Restricted Principle of Comprehension))
  • Corollary: Justification of Set Union (related to Axiom: Axiom of Union)
  • Corollary: Justification of Subsets and Supersets (related to Axiom: Schema of Separation Axioms (Restricted Principle of Comprehension))
  • Corollary: Justification of the Difference (related to Axiom: Schema of Separation Axioms (Restricted Principle of Comprehension))
  • Corollary: Justification of the Set-Builder Notation (related to Axiom: Schema of Separation Axioms (Restricted Principle of Comprehension))
  • Corollary: Limit of N-th Roots (related to Proposition: Rational Powers of Positive Numbers)
  • Corollary: Minimal Inductive Set Is Subset Of All Inductive Sets (related to Axiom: Axiom of Infinity)
  • Corollary: Monotony Criterion for Absolute Series (related to Proposition: Monotony Criterion)
  • Corollary: More Insight to Euler's Identity (related to Proposition: Special Values for Real Sine, Real Cosine and Complex Exponential Function)
  • Corollary: Negative Cosine and Sine vs Shifting the Argument (related to Proposition: Special Values for Real Sine, Real Cosine and Complex Exponential Function)
  • Corollary: Non-Cauchy Sequences are Not Convergent (related to Theorem: Completeness Principle for Real Numbers)
  • Corollary: Number of Vertices, Edges, and Faces of a Dual Graph (related to Definition: Dual Planar Graph)
  • Corollary: Order Relation for Natural Numbers is Strict Total (related to Proposition: Comparing Natural Numbers Using the Concept of Addition)
  • Corollary: Parallelogram - Defining Property I (related to Proposition: 1.34: Opposite Sides and Opposite Angles of Parallelograms)
  • Corollary: Parallelogram - Defining Property II (related to Proposition: 1.34: Opposite Sides and Opposite Angles of Parallelograms)
  • Corollary: Planarity of Subdivisions (related to Definition: Subdivision of a Graph)
  • Corollary: Primality of the Smallest Non-Trivial Divisor (related to Proposition: Existence of Prime Divisors)
  • Corollary: Prime Dividing Product of Primes Implies Prime Divisor (related to Lemma: Generalized Euclidean Lemma)
  • Corollary: Probability of Laplace Experiments (related to Definition: Laplace Experiments and Elementary Events)
  • Corollary: Probability of the Impossible Event (related to Proposition: Probability of the Complement Event)
  • Corollary: Properties of Transitive Sets (related to Definition: Transitive Set)
  • Corollary: Properties of a Real Scalar Product (related to Definition: Dot Product, Inner Product, Scalar Product (General Field Case))
  • Corollary: Properties of the Absolute Value (related to Definition: Absolute Value of Real Numbers (Modulus))
  • Corollary: Real Numbers Can Be Approximated by Rational Numbers (related to Proposition: Unique Representation of Real Numbers as `\(b\)`-adic Fractions)
  • Corollary: Real Polynomials of Odd Degree Have at Least One Real Root (related to Proposition: Limits of Polynomials at Infinity)
  • Corollary: Reciprocity Law of Falling And Rising Factorial Powers (related to Definition: Falling And Rising Factorial Powers)
  • Corollary: Reciprocity of Complex Exponential Function, Non-Zero Property (related to Proposition: Functional Equation of the Complex Exponential Function)
  • Corollary: Reciprocity of Exponential Function of General Base, Non-Zero Property (related to Proposition: Functional Equation of the Exponential Function of General Base)
  • Corollary: Reciprocity of Exponential Function, Non-Zero Property (related to Proposition: Functional Equation of the Exponential Function)
  • Corollary: Rectangle as a Special Case of a Parallelogram (related to Proposition: 1.34: Opposite Sides and Opposite Angles of Parallelograms)
  • Corollary: Reduction of `$\epsilon$`-NFA to DFA (related to Theorem: Reduction of `$\epsilon$`-NFA to NFA)
  • Corollary: Representing Real Cosine by Complex Exponential Function (related to Definition: Cosine of a Real Variable)
  • Corollary: Representing Real Sine by Complex Exponential Function (related to Definition: Sine of a Real Variable)
  • Corollary: Rhombus as a Special Case of a Parallelogram (related to Proposition: 1.34: Opposite Sides and Opposite Angles of Parallelograms)
  • Corollary: Rules for Exponentiation in a Group (related to Definition: Exponentiation in a Group)
  • Corollary: Rules of Calculations with Inequalities (related to Definition: Order Relation of Real Numbers)
  • Corollary: Set Difference and Set Complement are the Same Concepts (related to Axiom: Schema of Separation Axioms (Restricted Principle of Comprehension))
  • Corollary: Similar Triangles (related to Proposition: 1.32: Sum Of Angles in a Triangle and Exterior Angle)
  • Corollary: Simple Conclusions For Multiplicative Functions (related to Definition: Multiplicative Functions)
  • Corollary: Solutions of a Linear Equation with many Unknowns (related to Definition: Linear Equations with many Unknowns)
  • Corollary: Square as a Special Case of a Rhombus (related to Proposition: 1.46: Construction of a Square on a Given Segment)
  • Corollary: Strictly, Well-ordered Sets and Transitive Sets (related to Theorem: Mostowski's Theorem)
  • Corollary: Sufficient Condition for a Function to be Constant (related to Corollary: Estimating the Growth of a Function with its Derivative)
  • Corollary: Sum of Two Supplemental Angles Equals Two Right Angles (related to Proposition: 1.13: Angles at Intersections of Straight Lines)
  • Corollary: Sums, Products, and Powers Of Congruences (related to Proposition: Addition, Subtraction and Multiplication of Congruences, the Commutative Ring `$\mathbb Z_m$`)
  • Corollary: Taylor's Formula for Polynomials (related to Theorem: Taylor's Formula)
  • Corollary: The absolute value makes the set of rational numbers a metric space. (related to Definition: Absolute Value of Rational Numbers)
  • Corollary: The set of WHILE-computable functions is included in the set of partially WHILE-computable functions (related to Definition: WHILE-Computable Functions)
  • Corollary: The supplemental angle of a right angle is another right angle. (related to Definition: 1.10: Right Angle, Perpendicular Straight Lines)
  • Corollary: There is no set of all sets (related to Axiom: Schema of Separation Axioms (Restricted Principle of Comprehension))
  • Corollary: Triangulation of Quadrilateral and Sum of Angles (related to Proposition: 1.32: Sum Of Angles in a Triangle and Exterior Angle)
  • Corollary: Triangulation of an N-gon and Sum of Interior Angles (related to Proposition: 1.32: Sum Of Angles in a Triangle and Exterior Angle)
  • Corollary: Uniqueness of the Empty Set (related to Axiom: Axiom of Empty Set)
  • Corollary: Value of Zero to the Power of X (related to Proposition: Limits of General Powers)
  • Corollary: `\((-x)(-y)=xy\)` (related to Corollary: `\((-x)y=-(xy)\)`)
  • Corollary: `\((-x)y=-(xy)\)` (related to Proposition: Uniqueness of Negative Numbers)
  • Corollary: `\((x^{-1})^{-1}=x\)` (related to Proposition: Uniqueness of Inverse Real Numbers With Respect to Multiplication)
  • Corollary: `\(-(-x)=x\)` (related to Proposition: Uniqueness of Negative Numbers)
  • Corollary: `\(-0=0\)` (related to Proposition: Uniqueness of Negative Numbers)
  • Corollary: `\(0x=0\)` (related to Proposition: Distributivity Law For Real Numbers)
  • Corollary: `\(1^{-1}=1\)` (related to Proposition: Uniqueness of Inverse Real Numbers With Respect to Multiplication)
  • Definition: "Lies on" Relation
  • Definition: (Unit) Ring
  • Definition: (Weighted) Arithmetic Mean
  • Definition: 1.01: Point
  • Definition: 1.02: Line, Curve
  • Definition: 1.03: Intersections of Lines
  • Definition: 1.04: Straight Line, Segment and Ray
  • Definition: 1.05: Surface
  • Definition: 1.06: Intersections of Surfaces
  • Definition: 1.07: Plane
  • Definition: 1.08: Plane Angle
  • Definition: 1.09: Angle, Rectilinear, Vertex, Legs
  • Definition: 1.10: Right Angle, Perpendicular Straight Lines
  • Definition: 1.11: Obtuse Angle
  • Definition: 1.12: Acute Angle
  • Definition: 1.13: Boundary
  • Definition: 1.14: Plane Figure
  • Definition: 1.15: Circle, Circumference, Radius
  • Definition: 1.16: Center of the Circle
  • Definition: 1.17: Diameter of the Circle
  • Definition: 1.18: Semicircle
  • Definition: 1.19: Rectilinear Figure, Sides, n-Sided Figure
  • Definition: 1.20: Equilateral Triangle, Isosceles Triangle, Scalene Triangle
  • Definition: 1.21: Right Triangle, Obtuse Triangle, Acute Triangle
  • Definition: 1.22: Square, Rectangle, Rhombus, Rhomboid, Trapezium
  • Definition: 1.23: Parallel Straight Lines
  • Definition: 10.02: Magnitudes Commensurable and Incommensurable in Square
  • Definition: 2.1: Area of Rectangle, Rectangle Contained by Adjacent Sides
  • Definition: 2.2: Gnomon
  • Definition: 3.01: Congruent Circles
  • Definition: 3.02: Tangent to the Circle, Straight Line Touching The Circle
  • Definition: 3.03: Circles Touching One Another
  • Definition: 3.04: Chords Equally Far From the Center of a Circle
  • Definition: 3.05: Chords Being Further from the Center of a Circle
  • Definition: 3.06: Segment of a Circle, Arc
  • Definition: 3.07: Angle of a Segment
  • Definition: 3.08: Angle in the Segment (Inscribed Angle)
  • Definition: 3.09: Angle Standing Upon An Arc
  • Definition: 3.10: Circular Sector, Central Angle
  • Definition: 3.11: Similar Circular Segments
  • Definition: 4.1: Rectilinear Figure Inscribed in Another Rectilinear Figure
  • Definition: 4.2: Rectilinear Figure Circumscribed about Another Rectilinear Figure
  • Definition: 4.3: Inscribing Rectilinear Figures in Circles
  • Definition: 4.4: Circumscribing Rectilinear Figures about Circles
  • Definition: 4.5: Inscribing Circles in Rectilinear Figures
  • Definition: 4.6: Circumscribing Circles about Rectilinear Figures
  • Definition: 4.7: Chord and Secant
  • Definition: 5.01: Magnitude is Aliquot Part
  • Definition: 5.02: Multiple of a Real Number
  • Definition: 5.03: Ratio
  • Definition: 5.04: Having a Ratio
  • Definition: 5.05: Having the Same Ratio
  • Definition: 5.06: Proportional Magnitudes
  • Definition: 5.07: Having a Greater Ratio
  • Definition: 5.08: Proportion in Three Terms
  • Definition: 5.09: Squared Ratio
  • Definition: 5.10: Cubed Ratio
  • Definition: 5.11: Corresponding Magnitudes
  • Definition: 5.12: Alternate Ratio
  • Definition: 5.13: Inverse Ratio
  • Definition: 5.14: Composition of a Ratio
  • Definition: 5.15: Separation of a Ratio
  • Definition: 5.16: Conversion of a Ratio
  • Definition: 5.17: Ratio ex Aequali
  • Definition: 5.18: Perturbed Proportion
  • Definition: 6.01: Similar Rectilinear Figures
  • Definition: 6.02: Cut in Extreme and Mean Ratio
  • Definition: 6.03: Height of a Figure
  • Definition: 7.01: Unit
  • Definition: 7.02: Number
  • Definition: 7.03: Proper Divisor
  • Definition: 7.04: Aliquant Part, a Number Being Not a Divisor of Another Number
  • Definition: 7.05: Multiple, Number Multiplying another Number
  • Definition: 7.06: Even Number
  • Definition: 7.07: Odd Number
  • Definition: 7.08: Even-Times-Even Number
  • Definition: 7.09: Even-Times-Odd Number
  • Definition: 7.10: Odd-Times-Odd Number
  • Definition: 7.11: Prime Number
  • Definition: 7.12: Co-prime (Relatively Prime) Numbers
  • Definition: 7.13: Composite Number
  • Definition: 7.14: Not Co-prime Numbers
  • Definition: 7.15: Multiplication of Numbers
  • Definition: 7.16: Rectangular Number, Plane Number
  • Definition: 7.17: Cuboidal Number, Solid Number
  • Definition: 7.18: Square Number
  • Definition: 7.19: Cubic Number, Cube Number
  • Definition: 7.20: Proportional Numbers
  • Definition: 7.21: Similar Rectangles and Similar Cuboids, Similar Plane and Solid Numbers
  • Definition: 7.22: Perfect Number
  • Definition: Absolute Value of Complex Numbers
  • Definition: Absolute Value of Integers
  • Definition: Absolute Value of Rational Numbers
  • Definition: Absolute Value of Real Numbers (Modulus)
  • Definition: Absolute Values and Non-Archimedean Absolute Values of Fields
  • Definition: Absolutely Convergent Complex Series
  • Definition: Absolutely Convergent Series
  • Definition: Abstract Syntax Tree
  • Definition: Accumulation Point (Real Numbers)
  • Definition: Accumulation Points (Complex Numbers)
  • Definition: Addition of Complex Numbers
  • Definition: Addition of Ideals
  • Definition: Adjacency List Representation
  • Definition: Adjacency Matrix
  • Definition: Affine Basis, Affine Coordinate System
  • Definition: Affine Space
  • Definition: Affine Subspace
  • Definition: Affinely Dependent and Affinely Independent Points
  • Definition: Algebra over a Ring
  • Definition: Algebraic Element
  • Definition: Algebraic Structure (Algebra)
  • Definition: Algorithm (Effective Procedure)
  • Definition: Alternating Multilinear Map
  • Definition: Altitude of a Triangle
  • Definition: Ambiguous and Unambiguous Grammars
  • Definition: Argument of a Complex Number
  • Definition: Arithmetic Function
  • Definition: Associate
  • Definition: Associativity
  • Definition: Asymptotical Approximation
  • Definition: Automorphism
  • Definition: Average Velocity
  • Definition: Axioms
  • Definition: Basis, Coordinate System
  • Definition: Bernoulli Experiment
  • Definition: Biconnected Graphs, `\(k\)`-Connected Graphs
  • Definition: Big O Notation
  • Definition: Bijective Function
  • Definition: Bilinear Form
  • Definition: Binary Operation
  • Definition: Binomial Coefficients
  • Definition: Bipartite Graph
  • Definition: Boolean Algebra
  • Definition: Boundary Points, Closures, Interiors, and Exteriors
  • Definition: Bounded Affine Set
  • Definition: Bounded Complex Sequences
  • Definition: Bounded Complex Sets
  • Definition: Bounded Real Sequences, Upper and Lower Bounds for a Real Sequence
  • Definition: Bounded Sequence
  • Definition: Bounded Subset of a Metric Space
  • Definition: Bounded Subsets of Ordered Sets
  • Definition: Bounded Subsets of Unordered Sets
  • Definition: Bounded and Unbounded Functions
  • Definition: Cancellation Property
  • Definition: Canonical Normal Form
  • Definition: Canonical Projection
  • Definition: Canonical Representation of Natural Numbers, Factorization
  • Definition: Canonical Representation of Positive Rational Numbers
  • Definition: Carrier Set
  • Definition: Cartesian Product
  • Definition: Cauchy Sequence
  • Definition: Certain and Impossible Event
  • Definition: Characteristic of a Field
  • Definition: Characteristic of a Ring
  • Definition: Chromatic Number and `$k$`-Coloring of a Graph
  • Definition: Closed Curve, Open Curve
  • Definition: Closed Walks, Closed Trails, and Cycles
  • Definition: Closed and Open Regions of the Complex Plane
  • Definition: Closure
  • Definition: Co-prime Numbers
  • Definition: Coefficient Matrix
  • Definition: Collinear Points
  • Definition: Collinear Points, Segments, Rays
  • Definition: Column Vectors and Row Vectors
  • Definition: Combinations
  • Definition: Commutative (Abelian) Group
  • Definition: Commutative (Unit) Ring
  • Definition: Commutativity
  • Definition: Comparing the Elements of Posets and Chains
  • Definition: Comparison of Cardinal Numbers
  • Definition: Comparison of Filters, Finer and Coarser Filters
  • Definition: Complement Graph
  • Definition: Complete Bipartite Graph
  • Definition: Complete Graph
  • Definition: Complete Metric Space
  • Definition: Complete Ordered Field
  • Definition: Complete Residue System
  • Definition: Complete System of Representatives
  • Definition: Complex Cauchy Sequence
  • Definition: Complex Conjugate
  • Definition: Complex Infinite Series
  • Definition: Complex Polynomials
  • Definition: Complex Sequence
  • Definition: Composite Number
  • Definition: Composition of Binary Relations
  • Definition: Computational Problem, Solution
  • Definition: Concatenation of Languages
  • Definition: Concentric Circles
  • Definition: Concurrent Straight Lines
  • Definition: Conditional Probability
  • Definition: Congruence
  • Definition: Congruent, Residue
  • Definition: Conjugate Elements of a Group
  • Definition: Conjunction
  • Definition: Conjunctive and Disjunctive Canonical Normal Forms
  • Definition: Connected Vertices
  • Definition: Connected and Disconnected Graphs, Bridges and Cutvertices
  • Definition: Consistency and Negation-Completeness of a Logical Calculus
  • Definition: Constant Function
  • Definition: Constant Function Real Case
  • Definition: Contained Relation "`$\in_X$`"
  • Definition: Continued Fractions
  • Definition: Continuous Complex Functions
  • Definition: Continuous Function
  • Definition: Continuous Functions at Single Complex Numbers
  • Definition: Continuous Functions at Single Real Numbers
  • Definition: Continuous Functions in Metric Spaces
  • Definition: Continuous Random Variables
  • Definition: Continuous Real Functions
  • Definition: Continuously Differentiable Functions
  • Definition: Contrapositive
  • Definition: Convergent Complex Sequence
  • Definition: Convergent Complex Series
  • Definition: Convergent Rational Sequence
  • Definition: Convergent Real Sequence
  • Definition: Convergent Real Series
  • Definition: Convergent Sequences and Limits
  • Definition: Convex Affine Set
  • Definition: Convex Hull
  • Definition: Convex and Concave Functions
  • Definition: Coplanar Points and Straight Lines
  • Definition: Cosets
  • Definition: Cosine of a Real Variable
  • Definition: Cotangent Bundle
  • Definition: Countable Set, Uncountable Set
  • Definition: Curves In the Multidimensional Space `\(\mathbb R^n\)`
  • Definition: Cycle Graph
  • Definition: Cycles
  • Definition: Cyclic Group, Order of an Element
  • Definition: Cyclic, Acyclic Graph
  • Definition: Decagon
  • Definition: Decimal Representation of Real Numbers
  • Definition: Def. 10.01: Magnitudes Commensurable and Incommensurable in Length
  • Definition: Def. 10.03: Rational and Irrational Magnitudes
  • Definition: Def. 10.04: Rational and Irrational Magnitudes in Square
  • Definition: Def. 10.05: First Binomial
  • Definition: Def. 10.06: Second Binomial
  • Definition: Def. 10.07: Third Binomial
  • Definition: Def. 10.08: Fourth Binomial
  • Definition: Def. 10.09: Fifth Binomial
  • Definition: Def. 10.10: Sixth Binomial
  • Definition: Def. 10.11: First Apotome
  • Definition: Def. 10.12: Second Apotome
  • Definition: Def. 10.13: Third Apotome
  • Definition: Def. 10.14: Fourth Apotome
  • Definition: Def. 10.15: Fifth Apotome
  • Definition: Def. 10.16: Sixth Apotome
  • Definition: Def. 11.01: Solid Figures, Three-Dimensional Polyhedra
  • Definition: Def. 11.02: Surface of a Solid Figure
  • Definition: Def. 11.03: Straight Line at Right Angles To a Plane
  • Definition: Def. 11.04: Plane at Right Angles to a Plane
  • Definition: Def. 11.05: Inclination of a Straight Line to a Plane
  • Definition: Def. 11.06: Inclination of a Plane to a Plane
  • Definition: Def. 11.07: Similarly Inclined Planes
  • Definition: Def. 11.08: Parallel Planes
  • Definition: Def. 11.09: Similar Solid Figures
  • Definition: Def. 11.10: Equal Solid Figures
  • Definition: Def. 11.11: Solid Angle
  • Definition: Def. 11.12: Pyramid, Tetrahedron
  • Definition: Def. 11.13: Prism, Parallelepiped
  • Definition: Def. 11.14: Sphere
  • Definition: Def. 11.15: Axis of a Sphere
  • Definition: Def. 11.16: Center of a Sphere
  • Definition: Def. 11.17: Diameter of a Sphere
  • Definition: Def. 11.18: Cone
  • Definition: Def. 11.19: Axis of a Cone
  • Definition: Def. 11.20: Base of a Cone
  • Definition: Def. 11.21: Cylinder
  • Definition: Def. 11.22: Axis of a Cylinder
  • Definition: Def. 11.23: Bases of a Cylinder
  • Definition: Def. 11.24: Similar Cones, Similar Cylinders
  • Definition: Def. 11.25: Cube
  • Definition: Def. 11.26: Octahedron
  • Definition: Def. 11.27: Icosahedron
  • Definition: Def. 11.28: Dodecahedron
  • Definition: Definition of Complex Numbers
  • Definition: Definition of Irrational Numbers
  • Definition: Degree Sequence
  • Definition: Dense Sets, Nowhere Dense Sets
  • Definition: Dependent and Independent Absolute Values
  • Definition: Derivability Property
  • Definition: Derivative of an n-Dimensional Curve
  • Definition: Derivative, Differentiable Functions
  • Definition: Derived, Dense-in-itself, and Perfect Sets
  • Definition: Describing a Straight Line Using Two Vectors
  • Definition: Deterministic Finite Automaton (DFA)
  • Definition: Diagonal
  • Definition: Diagonal Matrix
  • Definition: Diameter In Metric Spaces
  • Definition: Difference Operator
  • Definition: Difference Quotient
  • Definition: Differentiable Manifold, Atlas
  • Definition: Differential Form of Degree k
  • Definition: Digraph, Initial and Terminal Vertices, Loops, Parallel and Inverse Edges, Simple Digraph
  • Definition: Dimension of a Vector Space
  • Definition: Dimension of an Affine Space
  • Definition: Diophantine Equations
  • Definition: Direct Product of Groups
  • Definition: Direct Sum of Vector Spaces
  • Definition: Directional Derivative
  • Definition: Discrete Random Variables
  • Definition: Discrete and Indiscrete Topology
  • Definition: Disjoint Sets
  • Definition: Disjunction
  • Definition: Divergent Sequences
  • Definition: Divergent Series
  • Definition: Divisibility of Ideals
  • Definition: Division of Real Numbers
  • Definition: Divisor, Complementary Divisor, Multiple
  • Definition: Divisor-Closed Sets
  • Definition: Domain of Discourse
  • Definition: Dot Product of Complex Numbers
  • Definition: Dot Product, Inner Product, Scalar Product (Complex Case)
  • Definition: Dot Product, Inner Product, Scalar Product (General Field Case)
  • Definition: Dual Planar Graph
  • Definition: Eigenvalue
  • Definition: Eigenvector
  • Definition: Elementary Gaussian Operations
  • Definition: Elementary Symmetric Functions
  • Definition: Ellipse
  • Definition: Embedding, Inclusion Map
  • Definition: Endomorphism
  • Definition: Epimorphism
  • Definition: Epsilon Non-Deteriministic Finite Automaton (`$\epsilon$`-NFA)
  • Definition: Equipotent Sets
  • Definition: Equivalence
  • Definition: Equivalence Class
  • Definition: Equivalence Relation
  • Definition: Equivalent Grammars
  • Definition: Euclidean Affine Space
  • Definition: Euclidean Movement - Isometry
  • Definition: Euclidean Ring, Generalization of Division With Quotient and Remainder
  • Definition: Euler function
  • Definition: Euler's Constant
  • Definition: Eulerian Graph
  • Definition: Eulerian Tour
  • Definition: Even Complex Sequence
  • Definition: Even and Odd Complex Functions
  • Definition: Even and Odd Functions
  • Definition: Even and Odd Numbers
  • Definition: Exclusive Disjunction
  • Definition: Existence of a Neutral Element
  • Definition: Exponential Function of General Base
  • Definition: Exponentiation in a Group
  • Definition: Exponentiation in a Monoid
  • Definition: Extended Real Numbers
  • Definition: Extensional Relation
  • Definition: Exterior Algebra, Alternating Product, Universal Alternating Map
  • Definition: Exterior, Interior, Alternate and Corresponding Angles
  • Definition: Face Degree
  • Definition: Face, Infinite Face
  • Definition: Factorial Polynomials
  • Definition: Factorial Ring, Generalization of Factorization
  • Definition: Falling And Rising Factorial Powers
  • Definition: Falling and Rising Factorial Powers of Functions
  • Definition: Field
  • Definition: Field Extension
  • Definition: Field Homomorphism
  • Definition: Finite Field
  • Definition: Finite Field Extension
  • Definition: Finite Set, Infinite Set
  • Definition: Finite and Infinite Graphs
  • Definition: Finite and Sigma-Finite Measure
  • Definition: Finite and Sigma-Finite Pre-measure
  • Definition: First and Second Category Sets
  • Definition: First-Order Ordinary Differential Equation (ODE)
  • Definition: Fixed Point, Fixed Point Property
  • Definition: Floor and Ceiling Functions
  • Definition: Formal Languages Generated From a Grammar
  • Definition: Frame of Reference
  • Definition: Function, Arity and Constant
  • Definition: Functional
  • Definition: Functional Equation
  • Definition: GOTO Command, GOTO Program, Index
  • Definition: GOTO-Computable Functions
  • Definition: Gaussian Method to Solve Systems of Linear Equations, Rank of a Matrix
  • Definition: Generalization of Divisor and Multiple
  • Definition: Generalization of the Greatest Common Divisor
  • Definition: Generalization of the Least Common Multiple
  • Definition: Generalized Polynomial Function
  • Definition: Generalized Union of Sets
  • Definition: Generating Set of a Group
  • Definition: Generating Set of an Ideal
  • Definition: Generating Systems
  • Definition: Geometric Mean
  • Definition: Geometric Probability
  • Definition: Geometric Progression, Continued Proportion
  • Definition: Girth and Circumference
  • Definition: Grammar (Syntax)
  • Definition: Graph Decomposable Into `\(k\)` Trees
  • Definition: Graph of a Function
  • Definition: Group
  • Definition: Group Homomorphism
  • Definition: Group Operation
  • Definition: Group Order
  • Definition: Hamiltonian Cycle
  • Definition: Hamiltonian Graph
  • Definition: Harmonic Series
  • Definition: Heine-Borel Property Defines Compact Subsets
  • Definition: Hereditary and Weakly Hereditary Properties
  • Definition: Hexagon
  • Definition: Higher Order Directional Derivative
  • Definition: Higher-Order Derivatives
  • Definition: Homeomorphism, Homeomorphic Spaces
  • Definition: Homomorphism
  • Definition: Hyperbolic Cosine
  • Definition: Hyperbolic Sine
  • Definition: Hyperplane of a Number Space
  • Definition: Ideal
  • Definition: Identity Function
  • Definition: Identity Matrix
  • Definition: Implication
  • Definition: Improper Integral
  • Definition: Incidence
  • Definition: Incidence, Adjacency, Neighbours
  • Definition: Incidence, Adjacency, Predecessor and Successor Vertices, Neighbours
  • Definition: Indefinite Sum, Antidifference
  • Definition: Independent Events
  • Definition: Index Set and Set Family
  • Definition: Indicator (Characteristic) Function, Carrier
  • Definition: Inductive Set
  • Definition: Inertial and Noninertial Frames of Reference
  • Definition: Infimum of Extended Real Numbers
  • Definition: Infimum, Greatest Lower Bound
  • Definition: Infinite Series, Partial Sums
  • Definition: Injective Function
  • Definition: Instantaneous Velocity
  • Definition: Integral Closure
  • Definition: Integral Element
  • Definition: Interior, Boundary, and Closures of a Region in the Complex Plane
  • Definition: Interlacing Pieces with Respect to a Cycle, Interlacement Graph
  • Definition: Interpretation of Propositions - the Law of the Excluded Middle
  • Definition: Interpretation of Strings of a Formal Language and Their Truth Function
  • Definition: Inverse Element
  • Definition: Inverse Relation
  • Definition: Invertible Functions, Inverse Functions
  • Definition: Invertible and Inverse Matrix
  • Definition: Irreducible Polynomial
  • Definition: Irreducible, Prime
  • Definition: Irreflexive, Asymmetric and Antisymmetric Binary Relations
  • Definition: Isolated Point (Real Numbers)
  • Definition: Isolated, Adherent, Limit, `$\omega$`-Accumulation and Condensation Points
  • Definition: Isometry
  • Definition: Isomorphic Digraphs
  • Definition: Isomorphic Undirected Graphs
  • Definition: Isomorphism
  • Definition: Iteration of Languages, Kleene Star, Kleene Plus
  • Definition: Jacobi Symbol
  • Definition: Jordan Arc (Simple Curve)
  • Definition: Knot
  • Definition: Knot Diagram, Classical Crossing, Virtual Crossing
  • Definition: LOOP Command, LOOP Program
  • Definition: LOOP-Computable Functions
  • Definition: Language
  • Definition: Laplace Experiments and Elementary Events
  • Definition: Leaf
  • Definition: Legendre Symbol
  • Definition: Limit Inferior
  • Definition: Limit Ordinal
  • Definition: Limit Superior
  • Definition: Limit of a Function
  • Definition: Limits and Accumulation Points of Sequences
  • Definition: Limits of Complex Functions
  • Definition: Limits of Real Functions
  • Definition: Linear Combination
  • Definition: Linear Equations with many Unknowns
  • Definition: Linear Function
  • Definition: Linear Map
  • Definition: Linear Span
  • Definition: Linearly Dependent and Linearly Independent Vectors, Zero Vector
  • Definition: Linked List, List Nodes
  • Definition: Literals, Minterms, and Maxterms
  • Definition: Local Extremum
  • Definition: Logarithmically Convex and Concave Functions
  • Definition: Logical Arguments
  • Definition: Logical Calculus
  • Definition: Magma
  • Definition: Manifold
  • Definition: Matrix Multiplication
  • Definition: Matrix and Vector Addition
  • Definition: Matrix, Set of Matrices over a Field
  • Definition: Maximal Ideal
  • Definition: Maximum (Real Numbers)
  • Definition: Measurable Set
  • Definition: Measurable Space
  • Definition: Measure
  • Definition: Measureable Function
  • Definition: Meter
  • Definition: Metric (Distance)
  • Definition: Metric Space
  • Definition: Minimal Inductive Set
  • Definition: Minimal Polynomial
  • Definition: Minimal Tree Decomposability
  • Definition: Minimum (Real Numbers)
  • Definition: Module
  • Definition: Modulo Operation for Real Numbers
  • Definition: Modulus of Continuity of a Continuous Function
  • Definition: Monoid
  • Definition: Monomorphism
  • Definition: Monotonic Functions
  • Definition: Monotonic Sequences
  • Definition: Mostowski Function and Collapse
  • Definition: Multilinear Map
  • Definition: Multiplication of Complex Numbers
  • Definition: Multiplication of Natural Numbers
  • Definition: Multiplicative Functions
  • Definition: Multiplicative System
  • Definition: Multiplicity of a Root of a Polynomial
  • Definition: Mutually Disjoint Sets
  • Definition: Mutually Exclusive and Collectively Exhaustive Events
  • Definition: Mutually Independent Events
  • Definition: Möbius Function, Square-free
  • Definition: Negation
  • Definition: Negation of a String
  • Definition: Neighborhood
  • Definition: Nested Real Intervals
  • Definition: Non-deterministic Finite Automaton (NFA)
  • Definition: Norm, Normed Vector Space
  • Definition: Normal Subgroups
  • Definition: Null Graph
  • Definition: Number `$\pi$`
  • Definition: Number of Divisors
  • Definition: Odd Complex Sequence
  • Definition: One-sided Derivative, Right-Differentiability and Left-Differentiability
  • Definition: Open Ball, Neighborhood
  • Definition: Open Cover
  • Definition: Open Function, Closed Function
  • Definition: Open Sets in Metric Spaces
  • Definition: Open and Closed Discs
  • Definition: Open and Closed Functions
  • Definition: Open, Closed, Clopen
  • Definition: Order Embedding
  • Definition: Order Relation for Integers - Positive and Negative Integers
  • Definition: Order Relation for Natural Numbers
  • Definition: Order Relation for Rational Numbers - Positive and Negative Rational Numbers
  • Definition: Order Relation for Step Functions
  • Definition: Order Relation of Real Numbers
  • Definition: Order of a Graph
  • Definition: Ordered Field
  • Definition: Ordered Pair, n-Tuple
  • Definition: Ordering of Topologies
  • Definition: Ordinal Number
  • Definition: Pairwise Independent Events
  • Definition: Paradox
  • Definition: Parallelogram - Defining Property III
  • Definition: Partial and Total Maps (Functions)
  • Definition: Pentagon
  • Definition: Perfect Number
  • Definition: Perfect Square
  • Definition: Periodic Functions
  • Definition: Permutations
  • Definition: Perspectivities
  • Definition: Pieces of a Graph With Respect to A Cycle
  • Definition: Planar Drawing (Embedding)
  • Definition: Planar Graph
  • Definition: Point of Division, Point of External Division
  • Definition: Points in a Coordinate System - Number Spaces
  • Definition: Points vs. Vectors in a Number Space
  • Definition: Points, Lines, Planes, Hyperplanes
  • Definition: Points, Straight Lines, and Planes
  • Definition: Pointwise and Uniform Convergence
  • Definition: Pointwise and Uniformly Convergent Sequences of Functions
  • Definition: Polynomial Ring
  • Definition: Polynomial over a Ring, Degree, Variable
  • Definition: Polynomials
  • Definition: Positive and Negative Parts of a Real-Valued Function
  • Definition: Power Set
  • Definition: Pre-measure
  • Definition: Predicate of a Logical Calculus
  • Definition: Preorder, Partial Order and Poset
  • Definition: Prime Field
  • Definition: Prime Ideal
  • Definition: Prime Numbers
  • Definition: Prime-Counting Function
  • Definition: Principal Ideal
  • Definition: Principal Ideal Domain
  • Definition: Principal Ideal Ring
  • Definition: Probability Distribution
  • Definition: Probability Mass Function
  • Definition: Probability and its Axioms
  • Definition: Products
  • Definition: Projectivities, Ranges and Pencils
  • Definition: Proofs and Theorems in a Logical Calculus
  • Definition: Quadratic Residue, Quadratic Nonresidue
  • Definition: Quantifier, Bound Variables, Free Variables
  • Definition: Quotient Set, Partition
  • Definition: Random Experiments and Random Events
  • Definition: Random Variable, Realization, Population and Sample
  • Definition: Ratio of Two Real Numbers
  • Definition: Rational Cauchy Sequence
  • Definition: Rational Functions
  • Definition: Rational Sequence
  • Definition: Real Absolute Value Function
  • Definition: Real Cauchy Sequence
  • Definition: Real Identity Function
  • Definition: Real Intervals
  • Definition: Real Sequence
  • Definition: Real Subsequence
  • Definition: Rearrangement of Infinite Series
  • Definition: Reciprocal Function
  • Definition: Recursive Definition of the Determinant
  • Definition: Reduced Residue System
  • Definition: Reduction of an Integer Polynomial Modulo a Prime Number
  • Definition: Reflexive, Symmetric and Transitive Binary Relations
  • Definition: Regular Graph
  • Definition: Regular Open, Regular Closed
  • Definition: Reidemeister Moves, Planar Isotopy Moves, Diagrammatic Moves
  • Definition: Relation
  • Definition: Relative and Absolute Frequency
  • Definition: Restriction
  • Definition: Riemann Sum With Respect to a Partition
  • Definition: Riemann-Integrable Functions
  • Definition: Ring Homomorphism
  • Definition: Ring of Integers
  • Definition: Ring of Sets (measure-theoretic definition)
  • Definition: Root, Degree of a Tree, Subtree, Height
  • Definition: Rules of Inference
  • Definition: Satisfaction Relation, Model, Tautology, Contradiction
  • Definition: Second
  • Definition: Section over a Base Space
  • Definition: Semantics of PL0
  • Definition: Semantics of a Formal Language
  • Definition: Semi-Eulerian Graph
  • Definition: Semi-Eulerian Tour, Open Trail
  • Definition: Semi-Hamiltonian Graph
  • Definition: Semi-Hamiltonian Path
  • Definition: Semigroup
  • Definition: Separating and Non-Separating Cycles
  • Definition: Sequence
  • Definition: Sequences Tending To Infinity
  • Definition: Set Complement
  • Definition: Set Difference
  • Definition: Set Intersection
  • Definition: Set Partition
  • Definition: Set Union
  • Definition: Set of Natural Numbers (Peano)
  • Definition: Set of Truth Values (True and False)
  • Definition: Set, Set Element, Empty Set
  • Definition: Set-theoretic Definition of Order Relation for Natural Numbers
  • Definition: Set-theoretic Definitions of Natural Numbers
  • Definition: Sets of Integers Co-Prime To a Given Integer
  • Definition: Sieve of Eratosthenes
  • Definition: Sieve, Sieve Problem
  • Definition: Sigma-Algebra
  • Definition: Signature
  • Definition: Signature of Propositional Logic - PL0
  • Definition: Signum Function in An Ordered Field
  • Definition: Similarity
  • Definition: Simplex
  • Definition: Sine of a Real Variable
  • Definition: Singleton
  • Definition: Size of a Graph
  • Definition: Solution of Ordinary DE
  • Definition: Solution to a Lower Triangular SLE - Forward Substitution
  • Definition: Solution to an Upper Triangular SLE - Backward Substitution
  • Definition: Soundness and Completeness of a Logical Calculus
  • Definition: Spacetime Diagram
  • Definition: Spanning Subgraph
  • Definition: Spanning Tree
  • Definition: Special Elements of Ordered Sets
  • Definition: Spectrum of a Commutative Ring
  • Definition: Square Matrix
  • Definition: Step Functions
  • Definition: Stirling Numbers of First and Second Kind
  • Definition: Strict Total Order, Strictly-ordered Set
  • Definition: Strings (words) over an Alphabet
  • Definition: Subadditive Function
  • Definition: Subbasis and Basis of Topology
  • Definition: Subdigraphs and Superdigraphs; Induced Subdigraph
  • Definition: Subdivision of a Graph
  • Definition: Subfield
  • Definition: Subgraphs and Supergraphs; Induced Subgraph
  • Definition: Subgroup
  • Definition: Subring
  • Definition: Subsequence
  • Definition: Subset and Superset
  • Definition: Subsets of Prime Numbers Not Dividing a Natural Number
  • Definition: Subspace
  • Definition: Substructure
  • Definition: Subtraction of Complex Numbers
  • Definition: Subtraction of Integers
  • Definition: Subtraction of Rational Numbers
  • Definition: Subtraction of Real Numbers
  • Definition: Sum of Angles
  • Definition: Sum of Divisors
  • Definition: Sums
  • Definition: Supplemental Angles
  • Definition: Suppressing Vertices, Suppressed Multigraph
  • Definition: Supremum Norm for Functions
  • Definition: Supremum of Extended Real Numbers
  • Definition: Supremum, Least Upper Bound
  • Definition: Surjective Function
  • Definition: Symmetric Bilinear Form
  • Definition: Symmetric Matrix
  • Definition: Syntax of PL0 - Propositions as Boolean Terms
  • Definition: Systems of Linear Equations with many Unknowns
  • Definition: Tangent Bundle
  • Definition: Tangent of a Real Variable
  • Definition: The Class of all Ordinals `$\Omega$`
  • Definition: Topological Chart
  • Definition: Topological Product, Product Topology
  • Definition: Topological Space, Topology
  • Definition: Topological Subspaces and Subspace Topologies
  • Definition: Topological Sum, Disjoint Union
  • Definition: Topological, Continuous, Open, and Closed Invariants
  • Definition: Total Order and Chain
  • Definition: Total and Unique Binary Relations
  • Definition: Totally Differentiable Functions, Total Derivative
  • Definition: Transcendental Element
  • Definition: Transition Map
  • Definition: Transitive Set
  • Definition: Transposed Matrix
  • Definition: Trees and Forests
  • Definition: Triangle
  • Definition: Triangle Numbers
  • Definition: Truth Table
  • Definition: Twin Prime Numbers
  • Definition: Type-0 (Phrase Structure) Grammars and Recursively Enumerable Languages
  • Definition: Type-1 (cs) Grammars and Context-sensitive Languages
  • Definition: Type-2 (cf) Grammars and Context-free Languages
  • Definition: Type-3 (Linear) Grammars and Regular Languages
  • Definition: Ultrafilter
  • Definition: Undirected Graph, Vertices, Edges, Simple Graph
  • Definition: Uniformly Continuous Functions (General Metric Spaces Case)
  • Definition: Uniformly Continuous Functions (Real Case)
  • Definition: Unit
  • Definition: Unit-Cost Random Access Machine
  • Definition: Unitary Affine Space
  • Definition: Universal Set
  • Definition: Unknot
  • Definition: Upper and Lower Triangular Matrix
  • Definition: Variable in a Logical Calculus
  • Definition: Vector Field
  • Definition: Vector Space
  • Definition: Vertex Degrees for Digraphs
  • Definition: Vertex Degrees for Undirected Graphs
  • Definition: Von Mangoldt Function
  • Definition: WHILE Command, WHILE Program
  • Definition: WHILE-Computable Functions
  • Definition: Walks, Trails, and Paths
  • Definition: Weakly and Strongly Connected Digraphs
  • Definition: Well-founded Relation
  • Definition: Well-order, Well-ordered Set
  • Definition: Zariski Topology of a Commutative Ring
  • Definition: Zero Divisor and Integral Domain
  • Definition: Zero Matrix, Zero Vector
  • Definition: Zero Ring
  • Definition: Zero of a Function
  • Definition: `$\mathcal P$`-Computable and `$\mathcal P$`-Decidable Problems
  • Definition: `$k$`-nary Connectives, Prime and Compound Propositions
  • Definition: `\(C^n\)` Differentiable Function
  • Definition: `\(C^{n}\)`-Diffeomorphism
  • Definition: `\(b\)`-Adic Fractions
  • Definition: `\(n\)` times Continuously Differentiable Functions
  • Definition: n-Periodical Complex Sequence
  • Epoch: 11th Century
  • Epoch: 12th Century
  • Epoch: 13th Century
  • Epoch: 14th Century
  • Epoch: 15th Century
  • Epoch: 16th Century
  • Epoch: 17th Century
  • Epoch: 18th Century
  • Epoch: 19th Century
  • Epoch: 20th Century
  • Epoch: 21th Century
  • Epoch: Ancient World (from 4000 BC to 1 BC)
  • Epoch: Early Middle Ages
  • Epoch: Late Ancient World (from 1 AD to 499 AD)
  • Epoch: Prehistory
  • Example: A digraph with a loop, and parallel and inverse edges (related to Definition: Digraph, Initial and Terminal Vertices, Loops, Parallel and Inverse Edges, Simple Digraph)
  • Example: A pointwise convergent sequence of functions, which is not uniformly convergent (related to Definition: Pointwise and Uniform Convergence)
  • Example: Analytical Thinking Joke (related to Part: Jokes)
  • Example: Applications of the Cauchy Condensation Criterion (related to Proposition: Cauchy Condensation Criterion)
  • Example: Bad Luck For People Suffering From Triskaidekaphobia (related to Part: Oddities and Curiosities)
  • Example: Difference Operators of Some Functions (related to Part: Discrete Calculus and Difference Equations)
  • Example: Divergent Alternating Sequence (related to Definition: Divergent Sequences)
  • Example: Divisibility Examples (related to Definition: Divisor, Complementary Divisor, Multiple)
  • Example: Example of Continuous Functions in Topological Spaces (related to Chapter: Continuity)
  • Example: Examples of ASTs (related to Part: Formal Languages)
  • Example: Examples of Absolute Values (related to Part: Ordered Fields and Their Topology)
  • Example: Examples of Accumulation Points (related to Definition: Accumulation Point (Real Numbers))
  • Example: Examples of Adjacency Matrices (related to Definition: Adjacency Matrix)
  • Example: Examples of Boolean Functions (related to Lemma: Boolean Function)
  • Example: Examples of Canonical Normal Forms (related to Chapter: Normal Forms in `$PL0$`)
  • Example: Examples of Computational Problems (related to Part: Computability)
  • Example: Examples of Convergent Sequences in Topological Spaces (related to Chapter: Sequences and Limits)
  • Example: Examples of Correct and Incorrect Negations of Implications (related to Lemma: Negation of an Implication)
  • Example: Examples of Cyclic Groups (related to Part: Group Theory)
  • Example: Examples of DFA (related to Chapter: Finite Automata (Finite Sequential Machines))
  • Example: Examples of Equivalence Relations (related to Definition: Equivalence Relation)
  • Example: Examples of Fields (related to Chapter: Fields (Overview))
  • Example: Examples of Functions Continuous at a Single Point (related to Definition: Continuous Functions at Single Real Numbers)
  • Example: Examples of Functions Not Continuous at a Single Point (related to Definition: Continuous Functions at Single Real Numbers)
  • Example: Examples of Functions in a Logical Calculus (related to Definition: Function, Arity and Constant)
  • Example: Examples of Group Homomorphisms (related to Definition: Group Homomorphism)
  • Example: Examples of Groups (related to Chapter: Groups (Overview))
  • Example: Examples of Important Arithmetic Functions (related to Chapter: Arithmetic Functions)
  • Example: Examples of Kernels and Images of Group Homomorphisms (related to Definition: Group Homomorphism)
  • Example: Examples of Languages (related to Definition: Language)
  • Example: Examples of Logical Arguments (related to Part: Methods of Mathematical Proving)
  • Example: Examples of Magmas, Semigroups, and Monoids (related to Chapter: Magmas, Semigroups, Monoids (Overview))
  • Example: Examples of Multinomial Coefficients (related to Proposition: Multinomial Coefficient)
  • Example: Examples of Multiplicative Functions (related to Definition: Multiplicative Functions)
  • Example: Examples of NFA (related to Chapter: Finite Automata (Finite Sequential Machines))
  • Example: Examples of Paradoxes (related to Definition: Paradox)
  • Example: Examples of Predicates in a Logical Calculus (related to Definition: Predicate of a Logical Calculus)
  • Example: Examples of Properties of Group Homomorphisms (related to Definition: Group Homomorphism)
  • Example: Examples of Propositions With a More Complex Syntax (related to Definition: Interpretation of Propositions - the Law of the Excluded Middle)
  • Example: Examples of Quantifiers in a Logical Calculus (related to Definition: Quantifier, Bound Variables, Free Variables)
  • Example: Examples of Real Functions, Whose Graphs Cannot be Plotted (related to Chapter: Types of Real Functions)
  • Example: Examples of Relations (related to Definition: Relation)
  • Example: Examples of Ring Homomorphisms (related to Chapter: Rings (Overview))
  • Example: Examples of Strings over Alphabets (related to Definition: Strings (words) over an Alphabet)
  • Example: Examples of Syntax (related to Definition: Grammar (Syntax))
  • Example: Examples of Variables in a Logical Calculus (related to Definition: Variable in a Logical Calculus)
  • Example: Examples of Vector Spaces (related to Definition: Vector Space)
  • Example: Examples of Well-founded Relations (related to Definition: Well-founded Relation)
  • Example: Examples of `$\epsilon$`-NFA (related to Chapter: Finite Automata (Finite Sequential Machines))
  • Example: Existence and Uniqueness of Solutions (related to Part: Methods of Mathematical Proving)
  • Example: Existence of not Riemann-Integrable Functions (related to Definition: Riemann-Integrable Functions)
  • Example: Fair Dice (related to Definition: Laplace Experiments and Elementary Events)
  • Example: Graph of a Real-Valued Function with One Variable (related to Definition: Graph of a Function)
  • Example: Is Reality Real? (related to Part: Jokes)
  • Example: Mentalist Trick (1) (related to Part: Tricks for Mental Maths)
  • Example: Mentalist Trick (2) (related to Part: Tricks for Mental Maths)
  • Example: Multiplying small numbers by 9 (related to Part: Tricks for Mental Maths)
  • Example: Pizza Lovers (related to Part: Jokes)
  • Example: Pointwise vs. Uniformly Convergent Sequences of Functions (related to Section: Uniform Convergence of Functions)
  • Example: Sexy Parabola (Joke) (related to Part: Jokes)
  • Example: Simulating More Complex Commands Using Basic `\(L O O P\)` Commands (related to Definition: LOOP Command, LOOP Program)
  • Example: Solution to a Degenerated Diagonal SLE (related to Section: Solving Simple Systems of Linear Equations)
  • Example: Solution to a Diagonal SLE (related to Section: Solving Simple Systems of Linear Equations)
  • Example: Solution to a Zero SLE (related to Section: Solving Simple Systems of Linear Equations)
  • Example: Some Other Examples Of Mostowski Functions and Collapses (related to Definition: Mostowski Function and Collapse)
  • Example: The Gaussian Method in Practice (related to Section: Solving General Systems Of Linear Equations - Gaussian Method)
  • Example: The Paper Box (related to Section: Various Dissection Puzzles)
  • Example: Trivial Subspaces, Zero Space (related to Definition: Subspace)
  • Example: What is time? (related to Part: Jokes)
  • Example: Working with Mostowski Functions and Collapses (related to Definition: Mostowski Function and Collapse)
  • Explanation: 1.1: Equality is an Equivalence Relation (related to Subsection: Common Notions (all Books))
  • Explanation: 1.2: Adding Equations Preserves Equality (related to Subsection: Common Notions (all Books))
  • Explanation: 1.3: Subtracting Equations Preserves Equality (related to Subsection: Common Notions (all Books))
  • Explanation: 1.4: Congruent Figures (related to Subsection: Common Notions (all Books))
  • Explanation: 1.5: Comparing the Size of Sets and Their Subsets (related to Subsection: Common Notions (all Books))
  • Explanation: A Note on Well-ordered Sets (related to Definition: Well-order, Well-ordered Set)
  • Explanation: All Types of Morphisms and Their Properties (related to Motivation: Common Concepts Of Algebra: Substructures and Morphisms)
  • Explanation: Building the Successors of Ordinal Numbers (related to Part: Ordinal Numbers)
  • Explanation: Calculation Rules in a Group with Additive Notation (related to Motivation: Calculations in a Group)
  • Explanation: Changing the Index Of Sums in Number Theory (related to Lemma: Möbius and Floor Functions Combined)
  • Explanation: Characteristic Zero Instead of Characteristic Infinite (related to Definition: Characteristic of a Ring)
  • Explanation: Chomsky's Hierarchy of Languages (related to Chapter: Classification of Formal Languages)
  • Explanation: Combinatorial Interpretation of Stirling Numbers of the First Kind (related to Part: Stirling Numbers)
  • Explanation: Combinatorial Interpretation of Stirling Numbers of the Second Kind (related to Part: Stirling Numbers)
  • Explanation: Comparison Between the Number Systems (related to Branch: Number Systems and Arithmetics)
  • Explanation: Connection Between the Cartesian Product and Functions Mapping Finite Sets into a Non-empty Set (related to Part: Set-theoretic Prerequisites Needed For Combinatorics)
  • Explanation: Connection Between the Power Set and Functions Mapping Sets into a Set with Two Elements (related to Part: Set-theoretic Prerequisites Needed For Combinatorics)
  • Explanation: Correct Negation of Statements (related to Part: Methods of Mathematical Proving)
  • Explanation: Deductive Reasoning (related to Chapter: Logical Arguments Used in Mathematical Proofs)
  • Explanation: Einstein's Interpretation of the Time Dilation (related to Proposition: Time Dilation, Lorentz Factor)
  • Explanation: Examples of Dual Statements for Planar Graphs (related to Chapter: Conditions for Planarity and Planarity Testing)
  • Explanation: Examples of Extensional Relations (related to Definition: Extensional Relation)
  • Explanation: Explanation of Congruence Classes (related to Definition: Congruent, Residue)
  • Explanation: Explanation of the Heine-Borel Property (related to Definition: Heine-Borel Property Defines Compact Subsets)
  • Explanation: Fourteen Sets Formed By Closure, Interior and Complement Operations (related to Chapter: Basic Topological Concepts)
  • Explanation: Geometrical Interpretation of Hyperplanes (related to Definition: Hyperplane of a Number Space)
  • Explanation: Good Practices for Writing Mathematical Proofs (related to Part: Methods of Mathematical Proving)
  • Explanation: Hasse Diagram (related to Chapter: Order Relations)
  • Explanation: How Functions interact with Set Operations (related to Lemma: Behavior of Functions with Set Operations)
  • Explanation: How a line is different from a solid and a surface? (related to Definition: 1.02: Line, Curve)
  • Explanation: How a point is different from a solid, a surface and a line? (related to Definition: 1.01: Point)
  • Explanation: How the Axiom of Separation Avoids Russel's Paradox (related to Axiom: Schema of Separation Axioms (Restricted Principle of Comprehension))
  • Explanation: How to Interpret Events Which Are Constructed From Other Events Doing Set Operations? (related to Definition: Random Experiments and Random Events)
  • Explanation: Indicator Function and Complete Induction (related to Part: Set-theoretic Prerequisites Needed For Combinatorics)
  • Explanation: Inductive Reasoning (related to Chapter: Invalid Logical Arguments)
  • Explanation: Jacobi Symbol vs. Solvability of Quadratic Congruences (related to Section: Generalizations of the Legendre symbol - Jacobi and Kronecker Symbols)
  • Explanation: Kernel and Image (related to Definition: Linear Map)
  • Explanation: Local Extrema on a Closed Interval (related to Proposition: Zero-Derivative as a Necessary Condition for a Local Extremum)
  • Explanation: Matrices of Linear Maps (related to Definition: Linear Map)
  • Explanation: Mutually Exclusive vs. Pairwise Independent Events (related to Definition: Pairwise Independent Events)
  • Explanation: Notes on Special Elements of Posets (related to Chapter: Order Relations)
  • Explanation: Operation Table (related to Part: Algebraic Structures - Overview)
  • Explanation: Pascal's Triangle (Triangle of Binomial Coefficients) (related to Definition: Combinations)
  • Explanation: Possibilities to Describe Sets, Venn-Diagrams, List, and Set-Builder Notations (related to Definition: Set, Set Element, Empty Set)
  • Explanation: Properties of the Pascal's Triangle (related to Explanation: Pascal's Triangle (Triangle of Binomial Coefficients))
  • Explanation: Representations of Binary Relations (related to Chapter: Binary Relations and Their Properties)
  • Explanation: Some Remarks on Functions (related to Chapter: Functions (Maps))
  • Explanation: Summary of Different Order Relations (related to Chapter: Order Relations)
  • Explanation: Transitive Set and Countability - Natural Numbers Have the Smallest Infinite Cardinality (related to Part: Cardinal Numbers)
  • Explanation: Unions of Subgroups Are Not Subgroups (related to Chapter: Groups (Overview))
  • Explanation: What does WLOG mean? (related to Part: Methods of Mathematical Proving)
  • Explanation: What does the Extensionality Principle mean? (related to Axiom: Axiom of Extensionality)
  • Explanation: When is something "well-defined" in mathematics? (related to Part: Methods of Mathematical Proving)
  • Explanation: Why did Euclid postulate the axiom of straight line determined by two points? (related to Axiom: 1.1: Straight Line Determined by Two Distinct Points)
  • Explanation: Why do the Peano axioms define natural numbers? (related to Axiom: Peano Axioms)
  • Explanation: Why is a random variable neither random, nor variable? (related to Definition: Random Variable, Realization, Population and Sample)
  • Explanation: Why is it impossible to divide by `\(0\)`? (related to Proposition: Definition of Real Numbers)
  • Index
  • Index: By Building Blocks
  • Index: By Contributors. Thank you!
  • Index: By Site Issues
  • Index: Content Tree
  • Index: Keyword
  • Index: Person
  • Index: Symbolic Notation
  • Index: Widgets
  • Lemma: A Criterion for Associates
  • Lemma: A Criterion for Valid Logical Arguments
  • Lemma: A proposition cannot be both, true and false
  • Lemma: A proposition cannot be equivalent to its negation
  • Lemma: Abel's Lemma for Testing Convergence
  • Lemma: Addition and Scalar Multiplication of Riemann Upper and Lower Integrals
  • Lemma: Affirming the Consequent of an Implication
  • Lemma: Any Positive Characteristic Is a Prime Number
  • Lemma: Any Set is Subset of Some Transitive Set - Its Transitive Hull
  • Lemma: Approximability of Continuous Real Functions On Closed Intervals By Step Functions
  • Lemma: Behavior of Functions with Set Operations
  • Lemma: Biconnectivity is a Necessary Condition for a Hamiltonian Graph
  • Lemma: Boolean Algebra of Propositional Logic
  • Lemma: Boolean Function
  • Lemma: Characterization of Closed Sets by Limits of Sequences
  • Lemma: Coloring of Trees
  • Lemma: Comparing the Elements of Strictly Ordered Sets
  • Lemma: Complex Numbers are Two-Dimensional and the Complex Numbers `\(1\)` and Imaginary Unit `\(i\)` Form Their Basis
  • Lemma: Composition of Functions
  • Lemma: Composition of Relations (Sometimes) Preserves Their Left-Total Property
  • Lemma: Composition of Relations Preserves Their Right-Uniqueness Property
  • Lemma: Construction of Conjunctive and Disjunctive Canonical Normal Forms
  • Lemma: Continuants and Convergents
  • Lemma: Convergence Test for Telescoping Series
  • Lemma: Convergent Rational Sequences With Limit `\(0\)` Are Rational Cauchy Sequences
  • Lemma: Convergent Rational Sequences With Limit `\(0\)` Are a Subgroup of Rational Cauchy Sequences With Respect To Addition
  • Lemma: Convergent Rational Sequences With Limit `\(0\)` Are an Ideal Of the Ring of Rational Cauchy Sequences
  • Lemma: Convergent Sequences are Cauchy Sequences (Metric Spaces)
  • Lemma: Coprimality and Congruence Classes
  • Lemma: Criteria for Convergent Sequences
  • Lemma: Cyclic Groups are Abelian
  • Lemma: De Morgan's Laws (Logic)
  • Lemma: Decreasing Sequence of Suprema of Extended Real Numbers
  • Lemma: Denying the Antecedent of an Implication
  • Lemma: Disjunctive Syllogism
  • Lemma: Distributivity of Conjunction and Disjunction
  • Lemma: Divisibility of Principal Ideals
  • Lemma: Division with Quotient and Remainder
  • Lemma: Dual Graph of a All Faces Contained in a Planar Hamiltonian Cycle is a Tree
  • Lemma: Elementary Gaussian Operations Do Not Change the Solutions of an SLE
  • Lemma: Equivalence of Different Descriptions of a Straight Line Using Two Vectors
  • Lemma: Equivalence of Set Inclusion and Element Inclusion of Ordinals
  • Lemma: Equivalency of Vectors in Vector Space If their Difference Forms a Subspace
  • Lemma: Euler's Identity
  • Lemma: Every Contraposition to a Proposition is a Tautology to this Proposition
  • Lemma: Every Proposition Implies Itself
  • Lemma: Factor Groups
  • Lemma: Factor Rings, Generalization of Congruence Classes
  • Lemma: Fiber of Maximal Ideals
  • Lemma: Fiber of Prime Ideals
  • Lemma: Fiber of Prime Ideals Under a Spectrum Function
  • Lemma: Finite Cardinal Numbers and Set Operations
  • Lemma: Functions Continuous at a Point and Non-Zero at this Point are Non-Zero in a Neighborhood of This Point
  • Lemma: Fundamental Lemma of Homogeneous Systems of Linear Equations
  • Lemma: Gaussian Lemma (Number Theory)
  • Lemma: Generalized Euclidean Lemma
  • Lemma: Greatest Common Divisor and Least Common Multiple of Ideals
  • Lemma: Group Homomorphisms and Normal Subgroups
  • Lemma: Handshaking Lemma for Finite Digraphs
  • Lemma: Handshaking Lemma for Finite Graphs
  • Lemma: Handshaking Lemma for Planar Graphs
  • Lemma: Hypothetical Syllogism
  • Lemma: Implication as a Disjunction
  • Lemma: Increasing Sequence of Infima of Extended Real Numbers
  • Lemma: Invertible Functions on Real Intervals
  • Lemma: It is true that something can be (either) true or false
  • Lemma: Kernel and Image of Group Homomorphism
  • Lemma: Kernel and Image of a Group Homomorphism are Subgroups
  • Lemma: LOOP-Computable Functions are Total
  • Lemma: Lem. 10.016: Incommensurability of Sum of Incommensurable Magnitudes
  • Lemma: Lem. 10.021: Medial is Irrational
  • Lemma: Lem. 10.028.1: Finding Two Squares With Sum Also Square
  • Lemma: Lem. 10.028.2: Finding Two Squares With Sum Not Square
  • Lemma: Lem. 10.032: Constructing Medial Commensurable in Square II
  • Lemma: Lem. 10.041: Side of Sum of Medial Areas is Irrational
  • Lemma: Lem. 10.053: Construction of Rectangle with Area in Mean Proportion to two Square Areas
  • Lemma: Lem. 10.059: Sum of Squares on Unequal Pieces of Segment Is Greater than Twice the Rectangle Contained by Them
  • Lemma: Lem. 10.13: Finding Pythagorean Magnitudes
  • Lemma: Lem. 11.23: Making a Square Area Equal to the Difference Of Areas of Two Other Incongruent Squares
  • Lemma: Lem. 12.02: Areas of Circles are as Squares on Diameters
  • Lemma: Lem. 12.04: Proportion of Sizes of Tetrahedra divided into Two Similar Tetrahedra and Two Equal Prisms
  • Lemma: Lem. 13.02: Converse of Area of Square on Greater Segment of Straight Line cut in Extreme and Mean Ratio
  • Lemma: Lem. 13.13: Construction of Regular Tetrahedron within Given Sphere
  • Lemma: Lem. 13.18: Angle of the Pentagon
  • Lemma: Linear Independence of the Imaginary Unit `\(i\)` and the Complex Number `\(1\)`
  • Lemma: Lower Bound of Leaves in a Tree
  • Lemma: Mixing-up the Inclusive and Exclusive Disjunction
  • Lemma: Mixing-up the Sufficient and Necessary Conditions
  • Lemma: Modus Ponens
  • Lemma: Modus Tollens
  • Lemma: Möbius and Floor Functions Combined
  • Lemma: Negation of an Implication
  • Lemma: One-to-one Correspondence of Ideals in the Factor Ring and a Commutative Ring
  • Lemma: Prime Ideals of Multiplicative Systems in Integral Domains
  • Lemma: Properties of Ordinal Numbers
  • Lemma: Rational Cauchy Sequences Build a Commutative Group With Respect To Addition
  • Lemma: Rational Cauchy Sequences Build a Commutative Monoid With Respect To Multiplication
  • Lemma: Reciprocity Law for Floor Functions
  • Lemma: Relationship between Tree Degree, Tree Height and the Number of Leaves in a Tree
  • Lemma: Riemann Integral of a Product of Continuously Differentiable Functions with Sine
  • Lemma: Sets of Integers Co-Prime to a given Integer are Divisor-Closed
  • Lemma: Sieve for Twin Primes
  • Lemma: Size of an `\(r\)`-regular Graph with `\(n\)` Vertices
  • Lemma: Splitting a Graph with Even Degree Vertices into Cycles
  • Lemma: Stirling Numbers and Rising Factorial Powers
  • Lemma: Subgroups and Their Cosets are Equipotent
  • Lemma: Subgroups of Cyclic Groups
  • Lemma: Successor of Ordinal
  • Lemma: Sum of Möbius Function Over Divisors With Division
  • Lemma: Sum of Roots Of Unity in Complete Residue Systems
  • Lemma: Sums of Floors
  • Lemma: The Proving Principle By Contraposition, Contrapositive
  • Lemma: The Proving Principle by Complete Induction
  • Lemma: The Proving Principle by Contradiction
  • Lemma: The Proving Principle by Transfinite Induction
  • Lemma: Trapezoid Rule
  • Lemma: Unique Valuation of Minterms and Maxterms
  • Lemma: Uniqueness Lemma of a Finite Basis
  • Lemma: Unit Circle
  • Lemma: Unit Ring of All Rational Cauchy Sequences
  • Lemma: Upper Bound for the Product of General Powers
  • Lemma: Upper Bound of Harmonic Series Times Möbius Function
  • Lemma: When is it possible to find a separating cycle in a biconnected graph, given a non-separating cycle?
  • Lemma: Zorn's Lemma
  • Motivation: Burali-Forti Paradox (related to Part: Ordinal Numbers)
  • Motivation: Calculations in a Group (related to Chapter: Groups (Overview))
  • Motivation: Cantor's Astonishing Discoveries Regarding the Cardinals of Infinite Sets (related to Part: Cardinal Numbers)
  • Motivation: Common Concepts Of Algebra: Substructures and Morphisms (related to Part: Algebraic Structures - Overview)
  • Motivation: Formulae of Negative Factorial Powers Explained (related to Definition: Falling And Rising Factorial Powers)
  • Motivation: Is "Being a Set Element" ("`$\in$`") a Relation? (related to Part: Ordinal Numbers)
  • Motivation: Measurement of the Speed of Light - First Experimental Proof that the Speed of Light is Finite (related to Part: Special Relativity)
  • Motivation: Michelson-Morley Experiment (related to Part: Special Relativity)
  • Motivation: Motivation for the Proof of Uniqueness of Zero (related to Proposition: Uniqueness of Negative Numbers)
  • Motivation: Observation 1: The Mostowski Function Produces Transitive Sets (related to Definition: Mostowski Function and Collapse)
  • Motivation: Observation 2: The Mostowski Function (Sometimes) Produces Relation Embeddings (related to Definition: Mostowski Function and Collapse)
  • Motivation: Rational Numbers and the Greatest Common Divisor (related to Chapter: Algebraic and Transcendent Numbers)
  • Motivation: Russell's Paradox (related to Branch: Set Theory)
  • Motivation: Significance of Equivalence Relations (related to Definition: Equivalence Relation)
  • Motivation: Usage of Ordered Tuples In Other Mathematical Disciplines (related to Part: Relations)
  • Motivation: What does not have to be proved in mathematics? (related to Part: Methods of Mathematical Proving)
  • Part: Additive Number Theory
  • Part: Algebraic Number Theory (Link)
  • Part: Algebraic Number Theory and Ring Theory
  • Part: Algebraic Structures - Overview
  • Part: Algebraic Topology
  • Part: Analytic Geometry
  • Part: Analytic Number Theory
  • Part: Basic Algorithms
  • Part: Basic Concepts of Logic
  • Part: Basics Concepts in Graph Theory
  • Part: Basics about Sets
  • Part: Calculus of Variations
  • Part: Cardinal Numbers
  • Part: Classical Physics
  • Part: Complex Analysis
  • Part: Complex Numbers
  • Part: Computability
  • Part: Computational Complexity Theory
  • Part: Constructions with Ruler and Compass
  • Part: Continuous Distributions
  • Part: Cycles, Permutations, Combinations and Variations
  • Part: Data Structures
  • Part: Differential Equations
  • Part: Differential Geometry
  • Part: Discrete Calculus and Difference Equations
  • Part: Discrete Distributions
  • Part: Dudeney's Amusements in Mathematics
  • Part: Elementary Number Theory
  • Part: Elliptic Geometry
  • Part: Estimation Theory
  • Part: Euclidean Geometry
  • Part: Extremal Problems in Graph Theory
  • Part: Finite Fields
  • Part: Flows
  • Part: Forgotten Reckoning Methods
  • Part: Formal Languages
  • Part: Functional Analysis
  • Part: Galois Theory
  • Part: General Relativity
  • Part: Graph Transformations
  • Part: Group Theory
  • Part: Gödel's Incompleteness Theorems
  • Part: Higher-Order Logics
  • Part: Historical Development of Analysis
  • Part: Historical Development of Combinatorics
  • Part: Historical Development of Geometry
  • Part: Historical Development of Logic
  • Part: Historical Development of Number Theory
  • Part: Historical Development of Set Theory
  • Part: Historical Development of Topology
  • Part: Homotopy
  • Part: Hyperbolic Geometry
  • Part: Infinite Graphs
  • Part: Integers
  • Part: Irrational Numbers
  • Part: Jokes
  • Part: Laws of Large Numbers
  • Part: Linear Algebra
  • Part: Linear Integral Equations
  • Part: Markov Chains
  • Part: Matchings
  • Part: Methods of Mathematical Proving
  • Part: Metric Spaces
  • Part: Multidimensional Random Variables
  • Part: Natural Numbers
  • Part: Network Design and Routing
  • Part: Numerical Algorithms
  • Part: Oddities and Curiosities
  • Part: Optimization Methods
  • Part: Ordered Fields and Their Topology
  • Part: Ordinal Numbers
  • Part: PL1 - First Order Predicate Logic
  • Part: Paths, Cycles and Connectivity
  • Part: Planar Graphs
  • Part: Projective Geometry
  • Part: Proof Theory
  • Part: Propositional Logic
  • Part: Quantum Field Theory
  • Part: Quantum Mechanics
  • Part: Randomness and Probability Calculus
  • Part: Rational Numbers
  • Part: Real Analysis of Multiple Variables
  • Part: Real Analysis of One Variable and Elements of Complex Analysis
  • Part: Real Numbers
  • Part: Relations
  • Part: Semi-numerical Algorithms
  • Part: Separation Of Topological Spaces
  • Part: Set-theoretic Prerequisites Needed For Combinatorics
  • Part: Solving Strategies and Sample Solutions Related to Arithmetics
  • Part: Solving Strategies and Sample Solutions Related to Number Theory
  • Part: Solving Strategies and Sample Solutions to Problems in Algebra
  • Part: Solving Strategies and Sample Solutions to Problems in Combinatorics
  • Part: Solving Strategies and Sample Solutions to Problems in Graph Theory
  • Part: Solving Strategies and Sample Solutions to Problems in Logic
  • Part: Solving Strategies and Sample Solutions to Problems in Set Theory
  • Part: Some Unsolved Number-Theoretic Problems
  • Part: Special Relativity
  • Part: Stirling Numbers
  • Part: The Basics Set-theoretic Topology
  • Part: Transitive Hull and Irreducible Kernels
  • Part: Tricks for Mental Maths
  • Part: Vector Analysis
  • Part: Vertex Colorings and Decompositions
  • Part: Zermelo-Fraenkel Set Theory
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  • Person: De Forest, Erastus Lyman
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  • Person: De Souza, Joaquim Gomes
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  • Person: Dedekind, Julius Wilhelm Richard
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  • Person: Dehn, Max Wilhelm
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  • Person: Dijksterhuis, Eduard Jan
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  • Person: Dirac, Paul Adrien Maurice
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  • Person: Dirksen, Enno Heeren
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  • Person: Droz-Farny, Arnold
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  • Person: Du Bois-Reymond, Paul
  • Person: Du Châtelet, Émilie
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  • Person: Duarte, Francisco José
  • Person: Dubickas, Artūras
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  • Person: Dubreil-Jacotin, Marie-Louise
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  • Person: Dye, Henry Abel
  • Person: Dynkin, Eugene Borisovich
  • Person: Dyson, Freeman John
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  • Person: Eckert, Wallace J.
  • Person: Eckmann, Beno
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  • Person: Edgeworth, Francis Ysidro
  • Person: Edmonds, Sheila May
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  • Person: Efimov, Nikolai Vladimirovich
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  • Person: Etherington, Ivor Malcolm Haddon
  • Person: Euclid Of Alexandria
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  • Person: Euwe, Machgielis
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  • Person: Feigenbaum, Mitchell Jay
  • Person: Feigl, Georg
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  • Person: Ferrari, Lodovico
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  • Person: Ferrers, Norman Macleod
  • Person: Ferro, del Scipione
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  • Person: Fields, John Charles
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  • Person: Fitzgerald, George Francis
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  • Person: Flamsteed, John
  • Person: Flato, Moshé
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  • Person: Flett, Thomas Muirhead
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  • Person: Floquet, Achille Marie Gaston
  • Person: Flügge, Wilhelm
  • Person: Flügge-Lotz, Irmgard
  • Person: Fock, Vladimir Aleksandrovich
  • Person: Focke, Anne Lucy Bosworth
  • Person: Fogels, Ernests
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  • Person: Fomin, Sergei Vasilovich
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  • Person: Gan De
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  • Person: Gershgorin, Semyon Aranovich
  • Person: Gerson, Rabbi Levi Ben
  • Person: Gerstner, František Josef
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  • Person: Gibson, George Alexander
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  • Person: Glaisher, James Whitbread Lee
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  • Person: Gohberg, Israel
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  • Person: Graham, Thomas
  • Person: Gram, Jorgen Pedersen
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  • Person: Kagan, Benjamin Fedorovich
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  • Person: Kendall, Maurice
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  • Person: Moisil, Grigore C
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  • Person: Nakano, Hidegorô
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  • Person: Nash, John Forbes
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  • Person: Nekrasov, Aleksandr Ivanovich
  • Person: Nelson, Evelyn Merle Roden
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  • Person: Nevanlinna, Rolf Herman
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  • Person: Nightingale, Florence
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  • Person: Nikolski, Serge Mikhalovich
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  • Person: Norlund, Niels Erik
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  • Person: O'Connell, Daniel
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  • Person: Obada, Abdel-Shafy
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  • Person: Ohm, Georg Simon
  • Person: Oka, Kiyoshi
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  • Person: Okikiolu, George Olatokunbo
  • Person: Okonjo, Chukwuka
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  • Person: Olubummo (2), Yewande
  • Person: Olubummo, Adegoke
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  • Person: Onicescu, Octav
  • Person: Oppenheim, Alexander Victor
  • Person: Ore, Øystein
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  • Person: Orlicz, Wladyslaw
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  • Person: Orshansky, Mollie
  • Person: Orszag, Steven Alan
  • Person: Oseen, C. Wilhelm
  • Person: Osgood, William Fogg
  • Person: Osipovsky, Timofei Fedorovic
  • Person: Ostrogradski, Mikhail Vasilevich
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  • Person: Ouedraogo, Marie Françoise
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  • Person: Paige, Constantin Marie Michel Hubert Jérôme Le
  • Person: Painlevé, Paul
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  • Person: Paley, Raymond Edward Alan Christopher
  • Person: Palis Jr, Jacob
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  • Person: Parry, William
  • Person: Pars, Leopold Alexander
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  • Person: Pascal, Étienne
  • Person: Pasch, Moritz
  • Person: Pask, Andrew Gordon Speedie
  • Person: Pastor, Julio Rey
  • Person: Pastur, Leonid Andreevich
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  • Person: Pauli, Wolfgang Ernst
  • Person: Pawlak, Zdzisław
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  • Person: Pedoe, Daniel
  • Person: Peierls, Rudolf Ernst
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  • Person: Pell, John
  • Person: Penney, William George
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  • Person: Perelman, Grigori Yakovlevich
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  • Person: Picard, Jean
  • Person: Pick, Georg Alexander
  • Person: Picken, David Kennedy
  • Person: Picone, Mauro
  • Person: Pier, Jean-Paul
  • Person: Pierce, Joseph
  • Person: Pieri, Mario
  • Person: Pierpont, James P
  • Person: Pillai, K. C. Sreedharan
  • Person: Pincherle, Salvatore
  • Person: Pinkerton, Peter
  • Person: Pisier, Jean Georges Gilles
  • Person: Pisot, Charles
  • Person: Pitiscus, Bartholomeo
  • Person: Pitman, Edwin James George
  • Person: Pitt, Harry Raymond
  • Person: Plana, Giovanni Antonio Amedeo
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  • Person: Planck, Max Karl Ernst Ludwig
  • Person: Plateau, Joseph Antoine Ferdinand
  • Person: Plato
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  • Person: Pleijel, Åke
  • Person: Plemelj, Josip
  • Person: Pless, Vera
  • Person: Plessner, Abraham Ezechiel
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  • Person: Plücker, Julius
  • Person: Pogorelov, Aleksei Vasilevich
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  • Person: Poinsot, Louis
  • Person: Poisson, Siméon Denis
  • Person: Pol, Balthasar van der
  • Person: Poleni, Giovanni
  • Person: Polkinghorne, John Charlton
  • Person: Pollaczek, Leo Félix
  • Person: Pollio, Marcus Vitruvius
  • Person: Polozii, Georgii Nikolaevich
  • Person: Pompeiu, Dimitrie
  • Person: Pompilj, Giuseppe
  • Person: Poncelet, Jean Victor
  • Person: Pontryagin, Lev Semenovich
  • Person: Popken, Jan
  • Person: Pople, John Anthony
  • Person: Popov, Blagoj Sazdov
  • Person: Popoviciu (2), Elena Moldovan
  • Person: Popoviciu, Tiberiu
  • Person: Poretsky, Platon Sergeevich
  • Person: Posidonius Of Rhodes
  • Person: Post, Emil Leon
  • Person: Postnikov, Mikhail Mikhailovich
  • Person: Potapov, Vladimir Petrovich
  • Person: Potts, Renfrey Burnard
  • Person: Poussin, Charles de la Vallée
  • Person: Povzner, Aleksandr Yakovlevich
  • Person: Praeger, Cheryl Elisabeth
  • Person: Prager, William
  • Person: Prandtl, Ludwig
  • Person: Prasad, Badri Nath
  • Person: Pratt, John Henry
  • Person: Preston, Gordon Bamford
  • Person: Price, Richard
  • Person: Prieto, Sotero
  • Person: Pringsheim, Alfred Israel
  • Person: Privalov, Ivan Ivanovich
  • Person: Prodi, Giovanni
  • Person: Prokhorov, Yurii Vasilevich
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  • Person: Prthudakasvami
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  • Person: Puiseux, Victor Alexandre
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  • Person: Pullar, John Robertson
  • Person: Puppini, Umberto
  • Person: Puri, Madan Lal
  • Person: Purser, John
  • Person: Pythagoras Of Samos
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  • Person: Péter, Rózsa
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  • Person: Qinglai, Xiong
  • Person: Qiujian, Zhang
  • Person: Quetelet, Lambert Adolphe Jacques
  • Person: Quillen, Daniel Gray
  • Person: Quine, Willard Van Orman
  • Person: Qushji, Ali
  • Person: Raabe, Joseph Ludwig
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  • Person: Rajagopal, Cadambathur Tiruvenkatacharlu
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  • Person: Ramanathan, Kollagunta Gopalaiyer
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  • Person: Ramanujan, Srinivasa Aiyangar
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  • Person: Ramsden, Jesse
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  • Person: Rao, Calyampudi Radhakrishna
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  • Person: Rayleigh), John William Strutt (Lord
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  • Person: Rees, Mina Spiegel
  • Person: Regiomontanus, Johann Müller
  • Person: Reichardt, Hans
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  • Person: Reidemeister, Kurt Werner Friedrich
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  • Person: Reinhardt, Karl August
  • Person: Reinher Of Paderborn
  • Person: Reinhold, Erasmus
  • Person: Reizins, Linards Eduardovich
  • Person: Rejewski, Marian Adam
  • Person: Rellich, Franz
  • Person: Remak, Robert Erich
  • Person: Remez, Evgeny Yakovlevich
  • Person: Remoundos, Georgios
  • Person: Rennie, Basil Cameron
  • Person: Reuter, Harry
  • Person: Reye, Karl Theodor
  • Person: Reynaud, Antoine-André-Louis
  • Person: Reyneau, Charles René
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  • Person: Rheticus, Georg Joachim von Lauchen
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  • Person: Riccati (3), Giordano
  • Person: Riccati, Jacopo Francesco
  • Person: Ricci (2), Michelangelo
  • Person: Ricci (3), Giovanni
  • Person: Ricci, Matteo
  • Person: Ricci-Curbastro, Gregorio
  • Person: Riccioli, Giovanni Battista
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  • Person: Richard, Louis
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  • Person: Richardson (3), Lewis Fry
  • Person: Richardson, Roland
  • Person: Richer, Jean
  • Person: Richmond, Herbert William
  • Person: Riemann, Georg Friedrich Bernhard
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  • Person: Riesz, Frigyes
  • Person: Rigby, John Frankland
  • Person: Righini, Guglielmo
  • Person: Ringrose, John Robert
  • Person: Ritt, Joseph Fels
  • Person: Rittenhouse, David
  • Person: Roach, Gary
  • Person: Robb, Richard Alexander
  • Person: Robbins, Herbert Ellis
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  • Person: Robertson (2), Edmund
  • Person: Robertson, Howard Percy
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  • Person: Robinson (3), Abraham
  • Person: Robinson (4), Julia Bowman
  • Person: Robinson, G. de B.
  • Person: Rocard, Yves-André
  • Person: Roch, Gustav
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  • Person: Rogers (2), Claude Ambrose
  • Person: Rogers, Leonard
  • Person: Rogosinski, Werner Wolfgang
  • Person: Rohn, Karl Friedrich Wilhelm
  • Person: Rohrbach, Hans
  • Person: Rokhlin, Vladimir Abramovich
  • Person: Rolle, Michel
  • Person: Romberg, Werner
  • Person: Rome, Adolphe
  • Person: Room, Thomas Gerald
  • Person: Rosanes, Jakob
  • Person: Rosellini, Ferdinando Pio
  • Person: Rosenberg, Fabian
  • Person: Rosenhain, Johann Georg
  • Person: Ross, Edward Burns
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  • Person: Roth, Leonard
  • Person: Rothblum, Uriel George
  • Person: Rothe, Erich Hans
  • Person: Rouché, Eugène
  • Person: Routh, Edward John
  • Person: Routledge, Norman Arthur
  • Person: Roux, Jean-Marie Le
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  • Person: Roy, Samarendra Nath
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  • Person: Rudin, Walter
  • Person: Rudio, Ferdinand
  • Person: Rudolff, Christoff
  • Person: Rudolph, Daniel Jay
  • Person: Ruffini, Paolo
  • Person: Rui, Li
  • Person: Rund, Hanno
  • Person: Runge, Carl David Tolmé
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  • Person: Russell (3), Alexander Durie
  • Person: Russell (4), Beulah
  • Person: Russell, John Scott
  • Person: Rutherford, Daniel Edwin
  • Person: Rutishauser, Heinz
  • Person: Rychlik, Karel
  • Person: Rydberg, Johannes Robert
  • Person: Rátz, Lászlo
  • Person: Rédei, László
  • Person: Rényi, Alfréd
  • Person: Réthy, Mór
  • Person: Różycki, Jerzy
  • Person: Saccheri, Giovanni Girolamo
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  • Person: Sadosky, Manuel
  • Person: Saint-Venant, Jean Claude
  • Person: Saitoti, George
  • Person: Saks, Stanisław
  • Person: Salaciense, Pedro Nunes
  • Person: Salem, Raphaël
  • Person: Salmon, George
  • Person: Samarskii, Alexander Andreevich
  • Person: Samelson, Hans
  • Person: Samoilenko, Anatoly Mykhailovych
  • Person: Sampson, Ralph Allen
  • Person: Samuel, Pierre
  • Person: Sanderson, Mildred
  • Person: Sang, Edward
  • Person: Sankara, Narayana
  • Person: Sansone, Giovanni
  • Person: Santaló, Luís Antoni
  • Person: Sargent, Winifred Lydia Caunden
  • Person: Sasaki, Shigeo
  • Person: Sato, Mikio
  • Person: Saunderson, Nicholas
  • Person: Saurin, Joseph
  • Person: Savage, Leonard Jimmie
  • Person: Savart, Félix
  • Person: Savary, Felix
  • Person: Savile, Sir Henry
  • Person: Sawyer, Warwick
  • Person: Schafer, Alice Turner
  • Person: Schatten, Robert
  • Person: Schattschneider, Doris
  • Person: Schauder, Juliusz Pawel
  • Person: Scheffers, Georg Wilhelm
  • Person: Scheffé, Henry
  • Person: Scheiner, Christoph
  • Person: Schelp, Richard Herbert
  • Person: Scherk, Heinrich Ferdinand
  • Person: Schickard, Wilhelm
  • Person: Schiffer, Menahem Max
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  • Person: Schlesinger, Ludwig
  • Person: Schläfli, Ludwig
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  • Person: Sylow, Peter Ludwig Mejdell
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  • Person: Szafraniec, Franciszek Hugon
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  • Person: Słupecki, Jerzy
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  • Person: Tamarkin, Jacob David
  • Person: Tanaka, Hideo
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  • Person: Terrot, Charles Hughes
  • Person: Tetens, Johannes Nikolaus
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  • Person: Theilheimer, Feodor
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  • Person: Theon Of Alexandria
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  • Person: Third, John Alexander
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  • Person: Thom, George
  • Person: Thomae, Carl Johannes
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  • Person: Thomson (4), William Leslie
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  • Person: Threlfall, William Richard Maximilian Hugo
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  • Problem: "Strand" Patience
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  • Problem: A Postoffice Perplexity
  • Problem: A Printer's Error
  • Problem: A Problem in Mosaics
  • Problem: A Problem in Squares
  • Problem: A Puzzle For Motorists
  • Problem: A Puzzle With Pawns
  • Problem: A Puzzle for Card-players
  • Problem: A Puzzle in Reversals
  • Problem: A Puzzling Legacy
  • Problem: A Puzzling Watch
  • Problem: A Queer Coincidence
  • Problem: