- From: Andreas Strotmann <strotman@cs.fsu.edu>
- Date: Fri, 22 Jun 2001 04:35:40 -0400 (EDT)
- To: Tim Bagot <tsb-w3-math-0001@earth.li>
- cc: <www-math@w3.org>
On Thu, 21 Jun 2001, Tim Bagot wrote:
> At 2001-06-21T09:59-0400, Andreas Strotmann wrote:-
>
> > for all x, +/-( x ) := one_of ({+x, -x}) .
>
> > The "one_of" construct fits nicely into the basic set of set-theoretic
> > operators, as it closely corresponds to the use of the axiom of choice.
>
> Interesting. I hadn't thought about it that way before. As an alternative,
> why not a map function to find the image of a set or list under a given
> function? This provides another way to avoid having to redefine operators,
> and would probably be useful elsewhere. Reuse of choices is a little
> harder this way, but not impossible.
There have been frequent discussions of the kind " why not use xyz instead
of zyx" on the OpenMath list at least. My stated opinion has always been
that everything that mathematicians regularly use as a concept, giving it
its own name, should find itself as a separate entry somewhere in MathML
and/or OpenMath. In this case, I would answer: introduce "map"
*in*addition* to one_of, not *instead*. Both encode important mathematical
concepts that are distinct, though related.
Incidentally, by adding MathML's bvar and condition qualifiers to a one_of
expression, one would get another useful variant: pick one of these
elements, but filter it according to the condition. In the case of "root
of a polynomial", for example, supposing it's defined interms of one_of,
one could easily express the concept of "positive real roots" or the
concept of "root near a point".
-- Andreas
Received on Friday, 22 June 2001 04:35:43 UTC