Definition of

Bijection

DRAFT (Not marked OK)

A pairing between two sets where:

• Every member of the first set is paired with exactly one member of the other set
• Every member of the other set is paired with exactly one member of the first set

This means:
* No two members of the first set map to the same member of the other set (injective or one-to-one)
* Every member of the other set is mapped to by some member of the first set (surjective or onto)

Bijective must be both injective and surjective.

Example: there is a bijection between the whole numbers and the even numbers.
* It is injective: if 2a=2b then a=b
* It is surjective: every even number y equals 2×(y/2)​, so it is paired to (y/2)