"image" v. "range" suddenly got a lot more important after it was found in the last century that the image set of a function might not be recursive. "Range"/"codomain" is important in computer science, where one would like to specify for a function an output data type which is capable of holding any value in the function's image; due to undecidability issues, it is good enough to specify a convenient superset of the image. At 01:01 PM 11/1/2011, Schroeppel, Richard wrote:

If you can't be sure about what's in the Image, it's still useful to know some superset. Perhaps the mistake is to speak of "the" range.

Rich

-----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Henry Baker Sent: Tuesday, November 01, 2011 1:45 PM To: math-fun@mailman.xmission.com Subject: [math-fun] function "image" v. function "range"

I noticed that the Khan Academy still uses the term "range" instead of "image" in order to describe the smallest (in terms of subsets) range for a function.

The "image" of f(x)=x*x (where the domain of f(x) is R) is {x in R|x>=0}. The "range" of f(x) is any superset of the image, e.g., R itself.

http://en.wikipedia.org/wiki/Image_%28mathematics%29

http://en.wikipedia.org/wiki/Range_%28mathematics%29

I assume that the Khan Academy teaches this usage for "range" because the standardized tests require it.

However, I thought that this usage of "range" was hopelessly obsolete, even 50 years ago.

Is this continuing usage of "range" instead of "image" an artifact of school budgets that still can't replace 50-year-old textbooks, or what?