bijection

• given any y in Y there exists x in X such that f(x)=y (f is surjective)
• given any a,b in X if f(a)=f(b) then a=b (f is injective)

An example of a bijection is the identity function 1_X:X->X that maps each x in X to itself.

An older, more human-readable name for a bijection is "one-to-one correspondence". However, as this is easily confused with "one-to-one function", the older name for an injection, mathematicians use the newer, more precise (but less friendly) terms.