Definition:
One-one, Onto, Bijection
- A function f from A to B is called one to one
(or one-one) if whenever f(a) = f(b) then a = b. Such functions
are also called injections.
- A function f from A to B is called onto if for
all b in B there is an a in A such that
f(a) = b. Such functions are also called surjections.
- A function f from A to B is called a bijection
if it is one to one and onto, i.e. bijections are functions that are
injective and surjective.
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