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.
Copyright
2000
Rensselaer Polytechnic Institute. All Rights Reserved.