bijective - перевод на русский
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bijective - перевод на русский

Bijective; One-to-one correspondence; Bijective map; Bijective mapping; Bijections; Bijectivity; Bijection (mathematics); Bijectional; Bijective function; One-to-one and onto; One to one correspondence; One to One Correspondence; 1-1 Correspondence; Bijective relation; One-one correspondence; 1-to-1 mapping; 1-to-1 map; Bijectio; Bijectiob; 1:1 correspondence; Bijective Function; Partial bijection; Partial one-one transformation; One to one and onto; 1-to-1 correspondence
  • A bijection from the [[natural number]]s to the [[integer]]s, which maps 2''n'' to −''n'' and 2''n'' − 1 to ''n'', for ''n'' ≥ 0.


общая лексика


взаимно однозначный

bijective function         


биективная функция

bijective mapping         


биективное отображение



<mathematics> A function is bijective or a bijection or a one-to-one correspondence if it is both injective (no two values map to the same value) and surjective (for every element of the codomain there is some element of the domain which maps to it). I.e. there is exactly one element of the domain which maps to each element of the codomain. For a general bijection f from the set A to the set B: f'(f(a)) = a where a is in A and f(f'(b)) = b where b is in B. A and B could be disjoint sets. See also injection, surjection, isomorphism, permutation. (2001-05-10)



In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set; there are no unpaired elements between the two sets. In mathematical terms, a bijective function f: XY is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y. The term one-to-one correspondence must not be confused with one-to-one function (an injective function; see figures).

A bijection from the set X to the set Y has an inverse function from Y to X. If X and Y are finite sets, then the existence of a bijection means they have the same number of elements. For infinite sets, the picture is more complicated, leading to the concept of cardinal number—a way to distinguish the various sizes of infinite sets.

A bijective function from a set to itself is also called a permutation, and the set of all permutations of a set forms the symmetric group.

Bijective functions are essential to many areas of mathematics including the definitions of isomorphisms, homeomorphisms, diffeomorphisms, permutation groups, and projective maps.