Surjective function

Written by Patrick Stevens last updated

A function is surjective if every has some such that . That is, its codomain is equal to its image.

This concept is commonly referred to as being "onto", as in "The function is onto."

Examples

  • The function (where is the set of natural numbers) given by is surjective. However, the same function viewed as a function is not surjective, because it does not hit the number , for instance.
  • The function given by is not surjective, because it does not hit the number , for instance: there is no such that .
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