6
$\begingroup$

According to my textbook:

A function which has either $\mathbb R$ or one of its subsets as its range is called a real valued function. Further, if its domain is also either $\mathbb R$ or a subset of $\mathbb R$, it is called a real function.

As there are 2 definitions here, is there a difference between "real functions" and "real-valued functions"?

MathWorld says that a real function is also called a real-valued function.

$\endgroup$
1
  • 1
    $\begingroup$ Each book should define the terms it will use. Especially if the meanings differ or are not well-known. $\endgroup$ – GEdgar Jan 1 '16 at 14:17
6
$\begingroup$

According to these definitions, any function $\mathbb C\to\mathbb R$ (for example, $z\mapsto |z|$) will be a real-valued function but not a real function.

As your research shows, this usage is not universal -- there can't be much disagreement about what a "real-valued function" is, but how the words "real function" are used can depend on the author and field.

$\endgroup$
1
  • $\begingroup$ Yes it's real valued but not a real function... $\endgroup$ – neelkanth Jan 1 '16 at 13:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.