I may be getting too old. I agree that John Denker's definition of a
function is what math profs are teaching these days. But it not what I
learned when I went to school.
When I studied math it was possible to have a multi-valued function.
The definition of function in use today is what we used to call a
"single-valued function." Since we used to have multi-valued functions
it was sometimes necessary to specify that a function be single-valued.
For example, all of my quantum-mechanics books say that one of the
criteria for determining permissable wave functions is that the function
must be single-valued. According to the current definition of function,
such a statement is meaningless.
In this regard I have a bit of a bone to pick with mathematicians. I
find that mathematicians sometimes just agree to change things without
checking (or even telling) people in fields that heavily use math. For
example, the Seventh Edition of Physical Chemistry by Peter Atkins (a
very popular book) just came out in 2002. In the quantum section it
says that psi must be a single-valued function. So Atkins, like many
physicists and chemists, does not yet know that there no longer is such
a thing as a multi-valued function. I only became aware of this because
I have tried to help my son and daughter with their math assignments.
They explained to me, "No dad, the curve you just drew is a relation,
not a function, don't you even know the basics?" Well, I did once, but
the basics seem to keep changing.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.