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 (2,499 words) - 18:57, 19 February 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 (2,199 words) - 13:37, 18 April 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) - 18:35, 12 April 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) - 11:38, 30 January 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 (2,670 words) - 06:51, 4 March 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) - 02:16, 30 March 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 (2,807 words) - 03:48, 17 May 2023 |
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... 30 KB (4,042 words) - 15:30, 9 April 2024 |
equivalent to counting injective functions N → X. Counting n-combinations of X is equivalent to counting injective functions N → X up to permutations... 43 KB (5,600 words) - 23:10, 4 February 2024 |
up inject, injected, injecting, injection, or injections in Wiktionary, the free dictionary. Injection or injected may refer to: Injective function, a... 2 KB (288 words) - 17:12, 27 March 2022 |
analysis, a holomorphic function on an open subset of the complex plane is called univalent if it is injective. The function f : z ↦ 2 z + z 2 {\displaystyle... 4 KB (608 words) - 22:03, 21 March 2024 |
Bijection (redirect from Bijective function) 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... 19 KB (2,503 words) - 00:11, 27 April 2024 |
Monomorphisms are a categorical generalization of injective functions (also called "one-to-one functions"); in some categories the notions coincide, but... 10 KB (1,362 words) - 10:20, 31 July 2023 |
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... 75 KB (11,220 words) - 03:46, 24 April 2024 |
space, is a local homeomorphism that is injective on A {\displaystyle A} , then f {\displaystyle f} is injective on some neighborhood of A {\displaystyle... 37 KB (6,894 words) - 05:50, 7 April 2024 |
Simple path may refer to: Simple curve, a continuous injective function from an interval in the set of real numbers R {\displaystyle \mathbb {R} } to R... 346 bytes (93 words) - 12:24, 3 February 2023 |
functions. A bi-Lipschitz function is a Lipschitz function φ : U → Rn which is injective and whose inverse function φ−1 : φ(U) → U is also Lipschitz. By Rademacher's... 19 KB (3,311 words) - 19:08, 21 April 2024 |
the pigeonhole principle, which states that there cannot exist an injective function from a larger finite set to a smaller finite set. Formally, a set... 22 KB (2,961 words) - 10:46, 20 April 2024 |
if and only if any of the following conditions hold: There is no injective function (hence no bijection) from X to the set of natural numbers. X is nonempty... 6 KB (826 words) - 03:33, 12 January 2024 |
is a specific type of function. These properties concern the domain, the codomain and the image of functions. Injective function: has a distinct value... 13 KB (1,407 words) - 21:21, 26 January 2023 |
Set (mathematics) (section Functions) unpaired elements. An injective function is called an injection, a surjective function is called a surjection, and a bijective function is called a bijection... 40 KB (4,659 words) - 18:33, 30 March 2024 |
Restriction (mathematics) (redirect from Function restriction) (respectively, a continuous map, etc.). The restriction of the non-injective function f : R → R , x ↦ x 2 {\displaystyle f:\mathbb {R} \to \mathbb {R}... 11 KB (1,924 words) - 04:32, 1 February 2024 |
may refer to: One-to-one function, also called an injective function One-to-one correspondence, also called a bijective function One-to-one (communication)... 2 KB (229 words) - 15:45, 26 March 2023 |
X} and Y {\displaystyle Y} if and only if there is an injective function but no bijective function from X {\displaystyle X} to Y {\displaystyle Y} . It... 22 KB (3,553 words) - 20:08, 24 April 2024 |
Inclusion map (redirect from Inclusion function) use this hooked arrow for any embedding.) This and other analogous injective functions from substructures are sometimes called natural injections. Given... 5 KB (587 words) - 23:02, 25 April 2024 |
Local diffeomorphism (category Theory of continuous functions) smooth immersion is a locally injective function while invariance of domain guarantees that any continuous injective function between manifolds of equal... 5 KB (670 words) - 22:18, 15 December 2022 |