A function that is both an injection and a surjection. if
f: X → Y
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.