◀ ▲ ▶Index / Index: By Contributors. Thank you!
Index: By Contributors. Thank you!
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- bookofproofs (8396)
- Branches
- History
- 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
- Person: 'sGravesande, Willem Jacob
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- Person: Abbe, Ernst
- Person: Abbott, Edwin
- Person: Abel, Niels Henrik
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- Person: Abhyankar, Shreeram Shankar
- Person: Abraham Ibn Ezra, ben Meir
- Person: Abraham, Max
- Person: Abramescu, Nicolae
- Person: Abu Kamil, ibn Aslam Shuja
- Person: Ackermann, Wilhelm
- Person: Adam, Pedro Puig
- Person: Adams (2), Edwin P.
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- Person: Adams (4), Frank
- Person: Adams, John Couch
- Person: Adamson, Iain Thomas Arthur Carpenter
- Person: Adelard Of Bath
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- Person: Valiron, Georges Jean Marie
- Person: Van Amringe, John Howard
- Person: Van Ceulen, Ludolph
- Person: Van Dantzig, David
- Person: Van Heuraet, Hendrik
- Person: Van Kampen, Egbert Rudolf
- Person: Van Lansberge, Johan Philip
- Person: Van Lint, Jacobus Hendricus
- Person: Van Roomen, Adriaan
- Person: Van Schooten, Frans
- Person: Van Vleck, Edward Burr
- Person: Vandermonde, Alexandre-Théophile
- Person: Vandiver, Harry Schultz
- Person: Vanstone, Ray
- Person: Varadhan, Sathamangalam Ranga Iyengar Srinivasa
- Person: Varahamihira
- Person: Varga (2), Richard Steven
- Person: Varga, Ottó
- Person: Varignon, Pierre
- Person: Varopoulos, Theodoros
- Person: Vashchenko-Zakharchenko, Mikhail Egorovich
- Person: Veblen, Oswald
- Person: Vekua, Ilya Nestorovich
- Person: Velez-Rodriguez, Argelia
- Person: Venn, John
- Person: Verbiest, Ferdinand
- Person: Verblunsky, Samuel
- Person: Verhulst, Pierre François
- Person: Vernier, Pierre
- Person: Vernon, Siobhan O'Shea
- Person: Veronese, Giuseppe
- Person: Verrier, Urbain Jean Joseph Le
- Person: Vessiot, Ernest-Paulin-Joseph
- Person: Viazovska, Maryna
- Person: Vidav, Ivan
- Person: Vietoris, Leopold
- Person: Vijayanandi
- Person: Vilant, Nicolas
- Person: Vince, Samuel
- Person: Vinogradov, Ivan Matveevich
- Person: Vinti, Calogero
- Person: Vitali, Giuseppe
- Person: Vitushkin, Anatoli Georgievich
- Person: Vivanti, Giulio
- Person: Viviani, Vincenzo
- Person: Viète, François
- Person: Vlacq, Adriaan
- Person: Vladimirov, Vasilii Sergeevich
- Person: Voevodsky, Vladimir Aleksandrovich
- Person: Volterra, Samuel Giuseppe Vito
- Person: Von Brill, Alexander Wilhelm
- Person: Von Dyck, Walther Franz Anton
- Person: Von Escherich, Gustav
- Person: Von Helmholtz, Hermann Ludwig Ferdinand
- Person: Von Koch, Niels Fabian Helge
- Person: Von Kármán, Theodore
- Person: Von Leibniz, Gottfried Wilhelm
- Person: Von Lindemann, Carl Louis Ferdinand
- Person: Von Mises, Richard
- Person: Von Nagel, Christian Heinrich
- Person: Von Neumann, John
- Person: Von Segner, Johann Andreas
- Person: Von Seidel, Philipp Ludwig
- Person: Von Staudt, Karl Georg Christian
- Person: Von Tschirnhaus, Ehrenfried Walter
- Person: Von Vega, Georg Freiherr
- Person: Voronoy, Georgy Fedoseevich
- Person: Vrănceanu, Gheorghe
- Person: Vályi, Gyula
- Person: Waerden, Bartel Leendert van der
- Person: Wald, Abraham
- Person: Wales, Muriel Kennett
- Person: Walfisz, Arnold
- Person: Walker (2), Gilbert
- Person: Walker (3), Geoffrey
- Person: Walker, John James
- Person: Wall, Hubert
- Person: Wallace (2), Alexander Doniphan
- Person: Wallace, William
- Person: Waller, Derek Arthur
- Person: Wallis, John
- Person: Walsh (2), Joseph
- Person: Walsh, John
- Person: Walter, Marion Ilse
- Person: Walton, Ernest
- Person: Wang, Hsien Chung
- Person: Wangerin, Friedrich Heinrich Albert
- Person: Wantzel, Pierre Laurent
- Person: Ward, Seth
- Person: Warga, Jack
- Person: Waring, Edward
- Person: Warner, Mary Wynne
- Person: Warschawski, Stefan E
- Person: Washington, Talitha
- Person: Waterston, John James
- Person: Watson (2), William
- Person: Watson (3), Henry William
- Person: Watson (4), George Neville
- Person: Watson, Henry
- Person: Watt, James
- Person: Wattie, James MacPherson
- Person: Wavre, Rolin
- Person: Wazewski, Tadeusz
- Person: Weatherburn, Charles Ernest
- Person: Weatherhead, Kenneth Kilpatrick
- Person: Weaver, Warren
- Person: Weber (2), Heinrich
- Person: Weber (3), Heinrich Friedrich
- Person: Weber (4), Johanna
- Person: Weber, Wilhelm Eduard
- Person: Wedderburn, Joseph Henry Maclagen
- Person: Wegner, Udo Hugo Helmuth
- Person: Weierstrass, Karl Theodor Wilhelm
- Person: Weil, André Abraham
- Person: Weiler, Adolf
- Person: Weingarten, Julius
- Person: Weinstein, Alexander
- Person: Weisbach, Julius Lugwig
- Person: Weise, Karl Heinrich
- Person: Welchman, William Gordon
- Person: Weldon, Walter Frank Raphael
- Person: Wending, Mei
- Person: Wenninger, Magnus Joseph
- Person: Werner (2), Wendelin
- Person: Werner, Johann
- Person: Wessel, Caspar
- Person: West, John
- Person: Weyl, Hermann Klaus Hugo
- Person: Weyr (2), Eduard
- Person: Weyr, Emil
- Person: Wheeler, Anna Johnson Pell
- Person: Whewell, William
- Person: Whish, Charles Matthew
- Person: Whiston, William
- Person: White, Henry Seely
- Person: Whitehead (2), Henry
- Person: Whitehead, Alfred North
- Person: Whiteside, Derek Thomas
- Person: Whitney, Hassler
- Person: Whitrow, Gerald
- Person: Whittaker (2), John
- Person: Whittaker, Edmund Taylor
- Person: Whitworth, Allen
- Person: Whyburn (2), William Marvin
- Person: Whyburn, William
- Person: Widder, David
- Person: Widman, Johannes
- Person: Wiegold, James
- Person: Wielandt, Helmut
- Person: Wiener (2), Hermann
- Person: Wiener (3), Ludwig Christian
- Person: Wiener (4), Norbert
- Person: Wiener, Christian
- Person: Wigner, Eugene Paul
- Person: Wilczynski, Ernest Julius
- Person: Wilder, Raymond Louis
- Person: Wiles, Andrew John
- Person: Wilf, Herbert Saul
- Person: Wilkins (2), J. Ernest
- Person: Wilkins, John
- Person: Wilkinson, James Hardy
- Person: Wilks, Samuel Stanley
- Person: William Of Ockham
- Person: Williams (2), Evan James
- Person: Williams (3), Lloyd
- Person: Williams, William Lloyd Garrison
- Person: Williamson, John
- Person: Wilson (2), John
- Person: Wilson (3), John
- Person: Wilson (4), Edwin
- Person: Wilson (5), Bertram
- Person: Wilson, Alexander
- Person: Wiltheiss, Ernst Eduard
- Person: Wilton, John Raymond
- Person: Wiman, Anders
- Person: Winkler, Wilhelm
- Person: Wintner, Aurel Friedrich
- Person: Wirtinger, Wilhelm
- Person: Wishart, John
- Person: Witt, Ernst
- Person: Witten, Edward
- Person: Wittgenstein, Ludwig Josef Johann
- Person: Wittich, Paul
- Person: Wolf (2), František
- Person: Wolf, Johann Rudolf
- Person: Wolfowitz, Jacob
- Person: Wolstenholme, Joseph
- Person: Womersley, John
- Person: Wood, Frances Chick
- Person: Woodard, Dudley Weldon
- Person: Woodhouse, Robert
- Person: Woods, Leslie Colin
- Person: Woodward, Robert Simpson
- Person: Wren (2), Thomas Lancaster
- Person: Wren, Sir Christopher
- Person: Wright (2), Edward Maitland
- Person: Wright (3), Fred
- Person: Wright, Sewall Green
- Person: Wrinch, Dorothy Maud
- Person: Wschebor-Wonsever, Mario Israel
- Person: Wu (2), Sijue
- Person: Wu, Wen-Tsun
- Person: Wussing, Hans
- Person: Wylie, Shaun
- Person: Xenocrates Of Chalcedon
- Person: Xian, Jia
- Person: Xiaotong, Wang
- Person: Yamabe, Hidehiko
- Person: Yang, Xiahou
- Person: Yano, Kentaro
- Person: Yasuaki, Aida
- Person: Yates, Frank
- Person: Yativrsabha
- Person: Yau, Shing-Tung
- Person: Yavanesvara
- Person: Yoccoz, Jean-Christophe
- Person: Yosida, Kosaku
- Person: Youden, William John
- Person: Young (2), William Henry
- Person: Young (3), Grace Chisholm
- Person: Young (4), Alfred
- Person: Young (5), Andrew
- Person: Young (6), Laurence Chisholm
- Person: Young (7), Lai-Sang
- Person: Young, Thomas
- Person: Youqin, Zhao
- Person: Yuan (2), Wang
- Person: Yuan, Ruan
- Person: Yue, Xu
- Person: Yule, George Udny
- Person: Yushkevich, Adolph Andrei Pavlovich
- Person: Zaanen, Adriaan Cornelis
- Person: Zalts, Karlis
- Person: Zarankiewicz, Kazimierz
- Person: Zaremba, Stanislaw
- Person: Zariski, Oscar
- Person: Zassenhaus, Hans Julius
- Person: Zeckendorf, Édouard
- Person: Zeeman, Erik Christopher
- Person: Zehfuss, Georg
- Person: Zelmanov, Efim Isaakovich
- Person: Zeno Of Elea
- Person: Zeno Of Sidon
- Person: Zenodorus
- Person: Zermelo, Ernst Friedrich Ferdinand
- Person: Zervos, Panagiotis
- Person: Zeuthen, Hieronymous Georg
- Person: Zhautykov, Orymbek
- Person: Zhi, Li
- Person: Zhukovsky, Nikolai Egorovich
- Person: Zi, Sun
- Person: Zippin, Leo
- Person: Zolotarev, Egor Ivanovich
- Person: Zorn, Max August
- Person: Zuse, Konrad
- Person: Zwicky, Fritz
- Person: Zygalski, Henryk
- Person: Zygmund, Antoni Szczepan
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- Person: Ávila, Artur
- Person: Öpik, Ernst
- Person: Čech, Eduard
- Person: Łoś, Jerzy Maria Michał
- Person: Łukasiewicz, Jan
- Person: Ślebarski, Tadeusz Boleslaw
- Person: Świerczkowski, Stanisław
- Person: Żorawski, Kazimierz
- Person: Żyliński, Eustachy
- Person: Țarină, Marian
- Problem: "Strand" Patience
- Problem: A Bank Holiday Puzzle
- Problem: A Calendar Puzzle
- Problem: A Census Puzzle
- Problem: A Chain Puzzle
- Problem: A Charitable Bequest
- Problem: A Chessboard Fallacy
- Problem: A Cutting-out Puzzle
- Problem: A Deal in Apples
- Problem: A Deal in Eggs
- Problem: A Dormitory Puzzle
- Problem: A Dungeon Puzzle
- Problem: A Family Party
- Problem: A Fence Problem
- Problem: A Juvenile Puzzle
- Problem: A Kite-flying Puzzle
- Problem: A Legal Difficulty
- Problem: A Lodging-house Difficulty
- Problem: A Magic Square Of Composites
- Problem: A Match Mystery
- Problem: A Mixed Pedigree
- Problem: A New Bishop's Puzzle
- Problem: A New Counter Puzzle
- Problem: A New Match Puzzle
- Problem: A New Money Puzzle
- Problem: A Packing Puzzle
- Problem: A Plantation Puzzle
- 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: