Range and Codomain of a RelationDate: 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/ |
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