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.
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Wikidata facts
- Subclass of
- injection
- Image
- Bijection.svg
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- Commons category
- Bijectivity
- different from
- injection
- has effect
- equinumerosity
- maintained by WikiProject
- WikiProject Mathematics
- facet of
- duality
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via Wikidata · CC0
Article · 日本語
数学において、全単射（ぜんたんしゃ）あるいは双射（そうしゃ）(bijective function, bijection) とは、写像であって、その写像の終域となる集合の任意の元に対し、その元を写像の像とする元が、写像の定義域となる集合に常にただ一つだけ存在するようなもの、すなわち単射かつ全射であるような写像のことを言う。例としては、群論で扱われる置換が挙げられる。 全単射であることを1対1上への写像[上への1対1写像] (one-to-one onto mapping)あるいは1対1対応 (one-to-one correspondence) ともいうが、紛らわしいのでここでは使用しない。 写像 f が全単射のとき、f は可逆であるともいう。
Abstract from DBpedia / Wikipedia · CC BY-SA