1. <mathematics> A function, f : A -> B, is injective or one-one, or is an injection, if and only if

for all a,b in A, f(a) = f(b) => a = b.

I.e. no two different inputs give the same output (contrast many-to-one).

This is sometimes called an embedding.

Only injective functions have left inverses f' where f'(f(x)) = x, since if f were not an injection, there would be elements of B for which the value of f' was not unique.