Dan, I too noticed this back in the 1960's, when I compared my calculus (engineering-oriented) book with my algebra book. Unfortunately, the calculus textbook people haven't been particularly careful about this particular issue -- it's only a matter of time before some major standardized test gets this particular thing wrong & creates more embarrassment for the mathematics community. Before condemning the calculus people too severely, it would be good to check historical usage -- I'm not sure that the algebra people would win the historical usage argument (even among mathematicians). After all, "range" for a gun or an airplane is the actual achievable distance, not the entire shooting range, or the list of all airports in the world. At 08:17 PM 3/18/2006, dasimov@earthlink.net wrote:
When I first learned the rigorous definition of a function f: X -> Y, the terminology was unequivocal: X is the domain of f, and Y is the range of f. The latter is unconditionally the case, irrespective of whether f is onto.
Nowadays, so many high school course and ill-considered calculus texts have redefined "range" to mean f(X) -- what I was taught is called the image of f -- that in teaching I've leaned away from using the word range to mean either thing.
Now I call the classical range by the term "codomain" (and I still call image "image").
It's a shame when the cognoscenti feel obliged to follow the ignorami.
--Dan