Encyclopedia > Function codomain

  Article Content

Function codomain

Given a function fA → B, the set B is called the codomain of f. The codomain is not to be confused with the range f(A), which is in general only a subset of B.


Let the function f be a function on the real numbers:

f: RR

defined by

f: xx2

The codomain of f is R, but clearly f(x) never takes negative values. The range is in fact the set R+ of non-negative reals, the interval [0,∞):

0 ≤ f(x) < ∞

One could have defined the function g thus:

g: RR+
g: xx2

While f and g have the same effect on a given number, they are not, in the modern view, the same function since they have different codomains.

The codomain can affect whether or not the function is a surjection; in our example, g is a surjection while f is not.

See also: Function domain

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article

... I[?] Ramses II ("The Great") Ramses III Ramses IV[?] The name means "Child of the Sun". This is a disambiguation page; that is, one that just points to other ...

This page was created in 22.2 ms