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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 
Associated Topics:
High School Functions

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