Перевод и анализ слов искусственным интеллектом ChatGPT
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- как употребляется слово
- частота употребления
- используется оно чаще в устной или письменной речи
- варианты перевода слова
- примеры употребления (несколько фраз с переводом)
- этимология
Что (кто) такое bijective - определение
![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.](https://commons.wikimedia.org/wiki/Special:FilePath/A bijection from the natural numbers to the integers.png?width=200 "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.")
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. In mathematical terms, a bijective function f: X → Y 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 isomorphism, homeomorphism, diffeomorphism, permutation group, and projective map.
![surjective]].](https://commons.wikimedia.org/wiki/Special:FilePath/Exponentiation as monoid homomorphism svg.svg?width=200 "surjective]].")
Википедия
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: X → Y 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.
