Set Size

Background
The notion of set size as the existence of a bijection was invented (discovered?) by Georg Cantor (1845 - 1918), the creator of modern set theory. Cantor was the son of a Danish merchant, Georg Waldemar Cantor. See Wikipedia for more information.

Definition
Quote from Wikipedia: When comparing two sets, we say that a set A and a set B have the same cardinality if and only if there exists a bijection, i.e. a one-to-one and onto function, between the two sets.

The same written in first order predicate logic:


 * $$|A|=|B| \Leftrightarrow$$


 * $$\exists f:A \to B ($$


 * $$\forall \; a,b \in A(a \neq b \to f(a) \neq f(b) )$$


 * $$\land \quad \forall \; b \in B \; ( \exists \; a \in A ( f(a) = b ) ) )$$