File:Bijection.svg · Wikimedia Commons · See Wikimedia Commons
Also known as bijective function, one-to-one correspondence, invertible function, bijective
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the codomain) is the image of exactly one element of the first set (the domain). Equivalently, a bijection is a relation between two sets such that each element of either set is paired with exactly one element of the other set.
A bijection is a mathematical pairing between two groups of objects where each item in one group matches with exactly one item in the other group, with no leftovers or duplicates on either side. This concept matters because it provides a precise way to establish when two collections have the same size, even when dealing with infinite sets, and serves as a foundation for understanding deeper mathematical relationships between different structures.
AI-generated from the Wikipedia summary — may contain errors.
Wikidata facts
- Subclass of
- injection
- Image
- Bijection.svg
Show 5 more facts
- Commons category
- Bijectivity
- different from
- injection
- has effect
- equinumerosity
- maintained by WikiProject
- WikiProject Mathematics
- facet of
- duality
Sources (3)
via Wikidata · CC0
Article · 中文
數學中，一個由集合映射至集合的函數，若對每一在內的，存在唯一一個在內的与其对应，且對每一在內的，存在唯一一個在內的与其对应，則此函數為對射函數。 換句話說，如果其為兩集合間的一一對應，则是雙射的。即，同時為單射和滿射。 例如，由整數集合至的函數，其將每一個整數連結至整數，這是一個雙射函數；再看一個例子，函數，其將每一對實數連結至，這也是個雙射函數。 一雙射函數亦簡稱為雙射（英語：bijection）或置換。後者一般較常使用在時。以由至的所有雙射組成的集合標記為。 雙射函數在許多數學領域扮演著很基本的角色，如在同構的定義（以及如同胚和等相關概念）、置換群、投影映射及許多其他概念的基本上。
Abstract from DBpedia / Wikipedia · CC BY-SA