title: "Bijection"

Bijection

Definition. A bijection is a Function that is both Injective and Surjective: a perfect pairing in which nothing is matched twice and nothing is left out.

Bijections are how set sizes are compared without counting: an infinite set is countable exactly when it admits a bijection with the positive integers (Lecture 2, Example 13, formalizing the lists of Lecture 2).