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...
16 KB (2,493 words) - 13:11, 1 June 2024
Bijection, injection and surjection (category Functions and mappings)
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...
15 KB (2,208 words) - 01:33, 2 May 2024
partial function which is injective. An injective partial function may be inverted to an injective partial function, and a partial function which is...
15 KB (2,041 words) - 21:03, 27 August 2024
Embedding (redirect from Locally injective function)
continuously differentiable function to be (among other things) locally injective. Every fiber of a locally injective function f : X → Y {\displaystyle f:X\to...
18 KB (2,676 words) - 10:02, 18 May 2024
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...
18 KB (2,182 words) - 21:42, 22 August 2024
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...
42 KB (5,165 words) - 00:52, 23 August 2024
Immersion (mathematics) (category Smooth functions)
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...
23 KB (2,861 words) - 01:58, 13 August 2024
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...
6 KB (616 words) - 18:36, 3 April 2024
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...
28 KB (4,375 words) - 23:54, 20 May 2024
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...
31 KB (4,141 words) - 12:35, 26 August 2024