Definition:Bijection

Definition
A mapping $$f: S \to T$$ is a bijection or bijective or a one(-to)-one correspondence iff $$f$$ is both a surjection and an injection.

If a bijection exists between two sets $$S$$ and $$T$$, then $$S$$ and $$T$$ are said to be in one-to-one correspondence.

It is clear that a bijection is a relation which is:
 * left-total;
 * right-total;
 * functional;
 * injective.