Math and science::Analysis::Tao::03: Set theory

Cardinality of sets

Equal cardinality

We say that two sets $$X$$ and $$Y$$ have equal cardinality iff [...].

Cardinality n

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.

Finite sets

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 $$X$$.