Difference between revisions of "Range"

Line 8: Line 8:
 
== See also ==
 
== See also ==
 
* [[Set notation]]
 
* [[Set notation]]
* [[Table of Contents]]
+
* [[AoPSWiki:Table of Contents]]
  
 
[[Category:Definition]]
 
[[Category:Definition]]

Revision as of 14:57, 8 January 2008

Let $A$ and $B$ be any sets and let $f:A\to B$ be any function between them, so that $A$ is the domain of $f$ and $B$ is the codomain. Then $\{b\in B\mid \mathrm{there\ is\ some\ } a\in A\mathrm{\ such\ that\ } f(a)=b\}$ is called the range or image of $f$.

Thus, if we have $f: \mathbb{R} \to \mathbb{R}$ given by $f(x) = x^2$, the range of $f$ is the set of nonnegative real numbers.


A function is a surjection exactly when the range is equal to the codomain.

See also