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July 2020

Injective function
In mathematics, an injective function (also known as injection, or one-to-one function) is a function that maps distinct elements of its domain to distinct
Surjective function
be unique; the function f may map one or more elements of X to the same element of Y. The term surjective and the related terms injective and bijective
Bijection, injection and surjection
but if g o f is injective, then it can only be concluded that f is injective (see figure). Every embedding is injective. A function is surjective (onto)
Partial function
partial function which is injective. An injective partial function may be inverted to an injective partial function, and a partial function which is
Function (mathematics)
An empty function is always injective. If X is not the empty set, and if, as usual, Zermelo–Fraenkel set theory is assumed, then f is injective if and only
one-to-one function (a.k.a. injective function) (see figures). An injective non-surjective function (injection, not a bijection) An injective surjective
Inverse function
not in the image. A function f with a left inverse is necessarily injective. In classical mathematics, every injective function f with a nonempty domain
Twelvefold way
equivalent to counting injective functions N → X. Counting n-combinations of X is equivalent to counting injective functions N → X up to permutations
Perfect hash function
an injective function. Perfect hash functions may be used to implement a lookup table with constant worst-case access time. A perfect hash function has
Identity function
function on M is clearly an injective function as well as a surjective function, so it is also bijective. The identity function f on M is often denoted by