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:

Definition: Equipotent Sets

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

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  1. Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001