Stumble ___ (discover by accident)

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In mathematics, injections, surjections and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other.

A function maps elements from its domain to elements in its codomain. Given a function f : X → Y {\displaystyle f\colon X\to Y} :

An injective function need not be surjective (not all elements of the codomain may be associated with arguments), and a surjective function need not be injective (some images may be associated with more than one argument). The four possible combinations of injective and surjective features are illustrated in the adjacent diagrams.

A function is injective (one-to-one) if each possible element of the codomain is mapped to by at most one argument. Equivalently, a function is injective if it maps distinct arguments to distinct images. An injective function is an injection. The formal definition is the following.

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