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   DIR Return to: Mathematics - General
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       #Post#: 86--------------------------------------------------
       Set Theory
   DIR By: Dragon Hellfire
       Date: March 29, 2019, 8:02 pm
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       Sets
       N: Natural Numbers
       I: Integers
       Q: Rational Numbers
       R: Real Numbers
       C: Complex Numbers
       Definitions
       Cardinality: The cardinality of a set is equal to the number of
       elements.
       Injective/One-To-One: A function such that each element of the
       codomain is mapped by at most one element of the domain.
       Surjective/Correspondence: A function such that each element of
       the codomain is mapped by at least one element of the domain.
       Bijective: A one-to-one correspondence.
       Countable Set: A set such that it is possible to create a
       bijection with some subset of the natural numbers.
       Theorems
       Theorem 1. The set of rational numbers is countable.
       Theorem 2. The set of real numbers is not countable.
       Theorem 3. R^2 and R have the same cardinality.
       Theorem 4. If there exist injective functions F: A->B and G:
       B->A, then there exists a bijection between A and B.
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