Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

Range and Codomain of a Relation

Date: 03/27/2004 at 01:04:22
From: Dinim
Subject: Range and codomain

What is the difference between the range and the codomian of a relation?



Date: 03/27/2004 at 17:09:51
From: Doctor Vogler
Subject: Re: Range and codomain

Hi Dinim,

Sometimes people use the term range to mean codomain.  When a person
distinguishes between the two, then "codomain" is the type of output
that the function was declared to produce.  That is, when you write

  f: A -> B,

then the codomain is B.  The range is the set of values that the
function actually takes on, that is f(A).  For example, the function

  f: R -> R

defined by

  f(x) = x^2

has for codomain the set of real numbers and for range the set of
nonnegative real numbers.

Of course, the codomain is only a matter of definition, since you
could declare exactly the same function as

  f: A -> f(A)

in order to make the codomain be the same as the range.

If you have any questions or need more help, please write back, and I
will try to offer further suggestions.

- Doctor Vogler, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
High School Functions

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/