bijection

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bijection (one-to-one onto function) A function that is both an injection and a surjection. If f : XY

is a bijection, then for each y in Y there is a unique x in X with the property that y = f(x)

i.e. there is a one-to-one correspondence between the elements in X and the elements in Y. The sets X and Y will have the same number of elements, i.e. the same cardinality. There will be a unique function f–1: Y X

such that f and f–1 are inverses to each other; f–1 will also be a bijection.