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injective function
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(Definition)
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We say that a function $f\colon A\to B$ is injective or one-to-one if $f(x)=f(y)$ implies $x=y$ or equivalently, whenever $x\neq y$ then $f(x)\neq f(y)$
- Suppose $A,B,C$ are sets and $f\colon A\to B$ $g\colon B\to C$ are injective functions. Then the composition $g\circ f$ is an injection.
- Suppose $f\colon A\to B$ is an injection, and $C\subseteq A$ Then the restriction $f|_C\colon C\to B$ is an injection.
For a list of other properties of injective functions, see [1].
- 1
- Wikipedia, article on Injective function.
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"injective function" is owned by drini. [ full author list (3) | owner history (1) ]
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Cross-references: restriction, composition, implies, function
There are 198 references to this entry.
This is version 11 of injective function, born on 2001-10-20, modified 2007-02-19.
Object id is 429, canonical name is InjectiveFunction.
Accessed 47008 times total.
Classification:
| AMS MSC: | 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory ) | | | 03E99 (Mathematical logic and foundations :: Set theory :: Miscellaneous) |
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Pending Errata and Addenda
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