injective function
We say that a function f:A→B is injective or one-to-one if f(x)=f(y) implies x=y, or equivalently, whenever x≠y, then f(x)≠f(y).
Properties
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1.
Suppose A,B,C are sets and f:A→B, g:B→C are injective functions. Then the composition
g∘f is an injection.
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2.
Suppose f:A→B is an injection, and C⊆A. Then the restriction
f|C:C→B is an injection.
For a list of other of injective functions, see [1].
References
- 1 Wikipedia, article on http://en.wikipedia.org/wiki/Injective_functionInjective function.
Title | injective function |
Canonical name | InjectiveFunction |
Date of creation | 2013-03-22 11:51:38 |
Last modified on | 2013-03-22 11:51:38 |
Owner | drini (3) |
Last modified by | drini (3) |
Numerical id | 16 |
Author | drini (3) |
Entry type | Definition |
Classification | msc 03E20 |
Classification | msc 03E99 |
Synonym | one-to-one |
Synonym | injection |
Synonym | embedding |
Synonym | injective |
Related topic | Bijection |
Related topic | Function |
Related topic | Surjective |