In mathematics, an injective function (also known as injection, or one-to-one function ) is a function f that maps distinct elements of its domain to...

g\circ f} is injective, then it can only be concluded that f {\displaystyle f} is injective (see figure). Every embedding is injective. A function is surjective...

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...

partial function which is injective. An injective partial function may be inverted to an injective partial function, and a partial function which is...

continuously differentiable function to be (among other things) locally injective. Every fiber of a locally injective function f : X → Y {\displaystyle f:X\to...

g(y)=g(f(h(y))=h(y)} . A function has a two-sided inverse if and only if it is bijective. A bijective function f is injective, so it has a left inverse...

natural numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in...

element x in the domain X. The identity function on X is clearly an injective function as well as a surjective function (its codomain is also its range), so...

function f itself need not be injective, only its derivative must be. A related concept is that of an embedding. A smooth embedding is an injective immersion...

A to B that is not injective, then no surjection from A to B is injective. In fact no function of any kind from A to B is injective. This is not true for...