# Injective

($1)$2 | $3 ($4) | $5 ($6)
Definition: Injective
A function is injective if, for all and , whenever , we have .
one-to-one is a synonym for injective.

A good way of thinking about injectivity is that the domain is "injected" into the codomain without being "compressed". In other words, no two (different) inputs go to the same output.

The following function is not injective:

because and are both 2 (but ).