Bijection, injection and surjection

Injections, surjections and bijections are three related ways of describing how a function relates its domain to its codomain. An injection, or one-to-one function, maps distinct elements of the domain to distinct elements of the codomain, so no two different inputs share an output. A surjection, or onto function, maps the domain so that every element of the codomain is the image of at least one element of the domain, meaning the function's image is the whole codomain. A bijection is a function that is both injective and surjective at once, pairing every element of the domain with exactly one element of the codomain and vice versa, which makes a bijection invertible. A function can be injective without being surjective, leaving some codomain elements unreached, or surjective without being injective, with several domain elements sharing an output; only a bijection achieves an exact one-to-one correspondence between the two sets. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/