Difference between revisions of "Surjection"

 
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A surjection is a function in which every value in its codomain is the function of a value of the domainA surjection is also referred to as an "on-to" function.
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A ''surjection'' is a [[function]] which takes each value in its [[codomain]] at some value in its [[domain]].  That is, the [[range]] (or [[image]]) of the function is equal to its codomain.  (For every function, the range is a subset of the codomain.) In adjectival form, we say that a function is ''surjective'' or ''onto''.
  
See also:
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For instance, the function <math>f: \mathbb Z \to \mathbb Z</math> defined by <math>f(x) = x+1</math> is surjective because for every [[integer]], there exists another integer one more than that integer, but the function <math>f: \mathbb N \to\mathbb N</math> defined by <math>f(x) = x+1</math> is not surjective because there exists a [[natural number]] which is not one more than any other natural number.
* [[bijection]]
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* [[injection]]
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==See also ==
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* [[Bijection]]
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* [[Injection]]
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Latest revision as of 21:39, 13 May 2020

A surjection is a function which takes each value in its codomain at some value in its domain. That is, the range (or image) of the function is equal to its codomain. (For every function, the range is a subset of the codomain.) In adjectival form, we say that a function is surjective or onto.

For instance, the function $f: \mathbb Z \to \mathbb Z$ defined by $f(x) = x+1$ is surjective because for every integer, there exists another integer one more than that integer, but the function $f: \mathbb N \to\mathbb N$ defined by $f(x) = x+1$ is not surjective because there exists a natural number which is not one more than any other natural number.

See also

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