Difference between revisions of "Range"
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Thus, if we have <math>f: \mathbb{R} \to \mathbb{R}</math> given by <math>f(x) = x^2</math>, the range of <math>f</math> is the set of [[nonnegative]] [[real number]]s. | Thus, if we have <math>f: \mathbb{R} \to \mathbb{R}</math> given by <math>f(x) = x^2</math>, the range of <math>f</math> is the set of [[nonnegative]] [[real number]]s. | ||
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A function is a [[surjection]] exactly when the range is equal to the codomain. | A function is a [[surjection]] exactly when the range is equal to the codomain. | ||
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== See also == | == See also == | ||
* [[Set notation]] | * [[Set notation]] | ||
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[[Category:Definition]] | [[Category:Definition]] | ||
Revision as of 22:02, 20 April 2008
Let 
and 
be any sets and let 
be any function between them, so that is the domain of 
and is the codomain. Then 
is called the range or image of .
Thus, if we have 
given by 
, the range of is the set of nonnegative real numbers.
A function is a surjection exactly when the range is equal to the codomain.
