Injection
Revision as of 14:48, 25 September 2007 by Valentin Vornicu (talk | contribs) (added some examples and an alternative definition)
An injection, or "one-to-one function," is a function that takes distinct values on distinct inputs. Equivalently, an injection is a function for which every value in the range is the image of exactly one value in the domain.
Alternative definition: A function is an injection if for all
, if
then
.
Examples
Linear functions are injections: ,
,
. The domain choosing is also important. For example, while
,
is not an injection (
), the function
,
, is an injection.
See also
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