When Georg Cantor studied sets at the end of the 19th century, he searched for a way to compare the number of elements between sets, which would fit for both, finite and infinite sets. He was the first to realize that the existence of a bijective map between the elements would do the trick. This motivates the following definition:
Two sets \(A\) and \(B\) are called equipotent, if and only if there is a bijective function \(f:A\to B\).
Lemmas: 1
Proofs: 2 3 4 5 6
Propositions: 7 8
Theorems: 9