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bijection
Sign in to saveAlso 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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~13 min read
Article
16 sectionsContents
- Definition
- Examples
- Batting line-up of a baseball or cricket team
- Seats and students of a classroom
- More mathematical examples
- Inverses
- Composition
- Cardinality
- Properties
- Category theory
- Generalization to partial functions
- Gallery
- See also
- Notes
- References
- External links
{{Dark mode invert|image=y|thumb|A bijective function, f: X → Y, where set X is {1, 2, 3, 4} and set Y is {A, B, C, D}. For example, f(1) = D.}}
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.