Cardinality of sets
We say that two sets \( X \) and \( Y \) have equal cardinality iff [...].
Let \( n \) be a natural number. A set \( X \) is said to have cardinality n if it has equal cardinality with the set [...]. We also say that such a set has \( n \) elements.
A set is finite iff [...] for some natural number \( n \); otherwise, the set is called infinite.
Notation: if \( X \) is a finite set, we use \( \#(X) \) to denote the cardinality of \( X \).