Injective function
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Injective function
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 distinct...
Bijection, injection and surjection
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...
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...
Immersion (mathematics)
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...
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...
Embedding
continuously differentiable function to be (among other things) locally injective. Every fiber of a locally injective function f : X → Y {\displaystyle f:X\to...
Inverse function
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...
Function (mathematics)
element. An empty function is always injective. If X is not the empty set, then f is injective if and only if there exists a function g : Y → X {\displaystyle...
Countable set
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...
Bijection
has the division by two as its inverse function. A function is bijective if and only if it is both injective (or one-to-one)—meaning that each element...