Definitions

Bijection

A bijection is a function which is both one-to-one and onto.

Function

A function ƒ is a relation of two sets Α and Β such that α Α , and β, γ Β
if (α, β) ƒ and (α, γ) ƒ, then β = γ.

One-to-One Function

A function is one-to-one if ƒ(x) = ƒ(y) implies that x = y.
Functions that are one-to-one are called Injections.

Onto Function

Given a function ƒ with a domain Α and range Β, a function is onto if y Β, there exists an x Α, such that ƒ(x) = y.
Functions that are onto are called Surjections.
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