A bijection is a bijective function. A function f:X->Y is said to be bijective iff:
  • 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 1X: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.

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