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>

Message-ID: <Pine.LNX.4.30.0106220422290.1566-100000@quake.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>

Message-ID: <Pine.LNX.4.30.0106220422290.1566-100000@quake.cs.fsu.edu>

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". -- AndreasReceived on Friday, 22 June 2001 04:35:43 UTC

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