Surjective function

Surjection. There is an arrow to every element in the codomain B from (at least) one element of the domain A.

In mathematics, a surjective or onto function is a function f : A → B with the following property. For every element b in the codomain B, there is at least one element a in the domain A such that f(a)=b. This means that no element in the codomain is unmapped, and that the range and codomain of f are the same set.^[1][2][3]

The term surjection and the related terms injection and bijection were introduced by the group of mathematicians that called itself Nicholas Bourbaki.^[4] In the 1930s, this group of mathematicians published a series of books on modern advanced mathematics. The French prefix sur means above or onto and was chosen since a surjective function maps its domain on to its codomain.

Not a surjection. No element in the domain A is mapped to the element {4} in the codomain B.

1. ↑ "The Definitive Glossary of Higher Mathematical Jargon". Math Vault. 2019-08-01. Retrieved 2020-09-08.
2. ↑ Weisstein, Eric W. "Surjection". mathworld.wolfram.com. Retrieved 2020-09-08.
3. ↑ C.Clapham, J.Nicholson (2009). "Oxford Concise Dictionary of Mathematics, Onto Mapping" (PDF). Addison-Wesley. p. 568. Retrieved 2014-01-01.
4. ↑ Miller, Jeff (2010). "Earliest Uses of Some of the Words of Mathematics". Tripod. Retrieved 2014-02-01.