Bijective in a sentence

A bijective map between two totally ordered sets that respects the two orders is an isomorphism in this category.

Also called an endomorphism of G. ; Automorphism : An endomorphism that is bijective, and hence an isomorphism.

Alternative (equivalent) formulations of the definition in terms of a bijective function or a surjective function can also be given.

A magma Q is a quasigroup precisely when all these operators, for every x in Q, are bijective.

Any bijective ring homomorphism is a ring isomorphism.

Bijective mapping from integer to even numbers To understand what this means, we first examine what it does not mean.

Euclidean transformations The Euclidean transformations or Euclidean motions are the ( bijective ) mappings of points of the Euclidean plane to themselves which preserve distances between points.

Every permutation of S has the codomain equal to its domain and is bijective and invertible.

For example, the symmetric group of a finite set consists of all bijective transformations of that set; thus, applying any element of the permutation group to an element of the set will produce another element of the set.

For finite sets, "permutations" and "bijective functions" refer to the same operation, namely rearrangement.

For instance, if g generates G, then so does h. This implies in particular that G and H are in bijective correspondence.

For instance, since a function is bijective if and only if it is both injective and surjective, in abstract algebra a homomorphism is an isomorphism if and only if it is both a monomorphism and an epimorphism.

In abstract algebra, several specific kinds of homomorphisms are defined as follows: * An isomorphism is a bijective homomorphism.

In this example it is not sufficient for a morphism to be bijective to be an isomorphism.

Its kernel is N. There is a bijective correspondence between the subgroups of G that contain N and the subgroups of G/N ; if H is a subgroup of G containing N, then the corresponding subgroup of G/N is π(H).

Mathematically a bijective function is used on the characters' positions to encrypt and an inverse function to decrypt.

One can prove that a ring homomorphism is an isomorphism if and only if it is bijective as a function on the underlying sets.

Particular bijective endofunctions are the involutions ; i.e., the functions coinciding with their inverses.

Properties * A function f: R → R is bijective if and only if its graph meets every horizontal and vertical line exactly once.

Properties of the category of sets The epimorphisms in Set are the surjective maps, the monomorphisms are the injective maps, and the isomorphisms are the bijective maps.