请输入您要查询的字词:

 

单词 Bijection
释义

bijection


Let X and Y be sets. A function f:XY that is one-to-one and onto is called a bijection or bijective function from X to Y.

When X=Y, f is also called a permutationMathworldPlanetmath of X.

An important consequence of the bijectivity of a function f is the existence of an inverse function f-1. Specifically, a function is invertiblePlanetmathPlanetmath if and only if it is bijectiveMathworldPlanetmath. Thus if f:XY is a bijection, then for any AX and BY we have

ff-1(B)=B
f-1f(A)=A

It easy to see the inverse of a bijection is a bijection, and that a compositionMathworldPlanetmath of bijections is again bijective.

Titlebijection
Canonical nameBijection
Date of creation2013-03-22 11:51:35
Last modified on2013-03-22 11:51:35
Ownermathcam (2727)
Last modified bymathcam (2727)
Numerical id16
Authormathcam (2727)
Entry typeDefinition
Classificationmsc 03-00
Classificationmsc 83-00
Classificationmsc 81-00
Classificationmsc 82-00
Synonymbijective
Synonymbijective function
Synonym1-1 correspondence
Synonym1 to 1 correspondence
Synonymone to one correspondence
Synonymone-to-one correspondence
Related topicFunction
Related topicPermutation
Related topicInjectiveFunction
Related topicSurjective
Related topicIsomorphism2
Related topicCardinalityOfAFiniteSetIsUnique
Related topicCardinalityOfDisjointUnionOfFiniteSets
Related topicAConnectedNormalSpaceWithMoreThanOnePointIsUncountable2
Related topicAConnectedNormalSpaceWithMoreThanOnePointIsUncountable
Related topicBo
随便看

 

数学辞典收录了18232条数学词条,基本涵盖了常用数学知识及数学英语单词词组的翻译及用法,是数学学习的有利工具。

 

Copyright © 2000-2023 Newdu.com.com All Rights Reserved
更新时间:2025/5/4 10:50:58