Bijection, injection and surjection

Common card · No. 226585

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} : The function is injective, or one-to-one, if each element of the codomain is mapped to by at most one element of the domain, or equivalently, if distinct elements of the domain map to distinct elements in the codomain. An injective function is also called an injection. Notationally: ∀ x , x ′ ∈ X , f ( x ) = f ( x ′ ) ⟹...

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