From: Andreas Strotmann <strotman@nu.cs.fsu.edu>

Date: Tue, 11 Apr 2000 20:07:15 -0400 (EDT)

To: David Eppstein <eppstein@ics.uci.edu>

cc: www-math@w3.org

Message-ID: <Pine.GSO.4.10.10004111936100.533-100000@xi.cs.fsu.edu>

Date: Tue, 11 Apr 2000 20:07:15 -0400 (EDT)

To: David Eppstein <eppstein@ics.uci.edu>

cc: www-math@w3.org

Message-ID: <Pine.GSO.4.10.10004111936100.533-100000@xi.cs.fsu.edu>

> > > Thoughts? Are there any other ommissions that > > stand out for you? Even though the question wasn't meant for me in particular, there are a couple of things (some of which I mentioned before, I believe) that do stand out: 1. Cartesian product of sets as well as the notion of tuple (as opposed to the vector notion which has been used as a substitute in examples submitted on this list). Why vector is not the right thing to use instead of tuple? Because vector implies the notion of a vector space, with metrics and all that stuff. It also implies uniform elements, so that the many common cases of mixed-type operations would be awkward. In a nut-shell, neither list nor vector nor any other type available in MathML appears to denote the fundamental concept of tuple. It should therefore be added. 2. Curiously, the application operator <application/> is actually missing, too - the one that denotes the operation of applying one thing to something else. Again, this is a fundamental concept that certainly needs to be discussed in k-12 (and again in more depth in introductory college math and computer science), and thus needs to be present in MathML, especially since <apply> </apply> now has a much broader meaning. In math and CS, the concept of function application is required as a separate operator in particular when reasoning about the <lambda/> construct, I suppose. (The argument for an <application/> different from <apply> </apply> is thus closely similar to the argument for using <sin/> etc instead of <sin> ...</sin> given in the MathML document). 3. Similarly, MathML terms for the fundamental concepts <function/>, <set/>, <quantifier/>, <predicate/> etc., all of which are extensively discussed and used in k-12 math literature, are missing. I realize that I'm advocating here the introduction of mathematical concepts into MathML that do not have a default rendering, but it is well within the scope of MathML to provide the fundamental vocabulary necessary for providing content markup for the basics of Maths. -- AndreasReceived on Tuesday, 11 April 2000 20:07:17 UTC

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