Part: Cardinal Numbers
In this part, we will be dealing with cardinal nubers or short cardinals. Cardinals are a mathematical clarification of the intuitive concept of how many elements a set has. For finite sets, it is possible to "count" the elements and tell the number corresponding to the number of elements in this set, or its cardinality. It turns out that cardinals represent the cardinalities of both, finite and infinite sets. But not only this. Cardinals do not only represent the cardinalities of other sets of but they are sets themselves. In the following text, we will see, how this all fits together.
Table of Contents
Motivations: 1 Explanations: 1
 Definition: Equipotent Sets
 Proposition: Cardinal Number
 Definition: Finite Set, Infinite Set
 Definition: Comparison of Cardinal Numbers
 Chapter: Can Cardinals be Ordered?
 Theorem: SchröderBernstein Theorem
 Chapter: Simple Facts Regarding Cardinals
 Definition: Countable Set, Uncountable Set
 Proposition: Union of Countably Many Countable Sets
 Proposition: Cardinals of a Set and Its Power Set
 Proposition: Subset of a Countable Set is Countable
 Proposition: Rational Numbers are Countable
 Proposition: Real Numbers are Uncountable
 Proposition: Uncountable and Countable Subsets of Natural Numbers
 Chapter: Continuum Hypothesis
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Chapters: 1
Parts: 2
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