bijection

A pairing between two sets that matches every element of one to exactly one element of the other, with nothing left over.

A bijection between finite sets $A$ and $B$ is a pairing that is both one-to-one (no element of $B$ paired twice) and onto (every element of $B$ is paired); it forces $|A|=|B|$ .

Examples

Subsets of an n-set pair with length-n binary strings, so there are $2^n$ subsets.