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Re: A few questions/suggestions about MathML 2.0

From: Andreas Strotmann <strotman@nu.cs.fsu.edu>
Date: Tue, 29 Feb 2000 15:58:11 -0500 (EST)
To: David Carlisle <davidc@nag.co.uk>
cc: Jerome.Euzenat@inrialpes.fr, www-math@w3.org
Message-ID: <Pine.GSO.4.10.10002291537280.29241-100000@xi.cs.fsu.edu>
> For MathML2 we now plan to deprecate the existing usage of set with
> _just_ a bound variable and a condition and instead make the
> set constructor take one or more bvar elements specifying bound
> variables (x and y in your example) a condition element specifying
> the predicate  ( x\in A /\ y\in B  here) and (new) the remaining
> child being an expression in the bound variables for constructing the
> elements of the set.  <x,y> here. The current usage where the
> last expression is omitted, and the set ranges over the bound variable
> will be deprecated. (Note this is only a plan at present, we have
> to see how this would affect other parts of MathML, and existing MathML
> systems.)

Very good!  I hope that that means you're also planning to deprecate the
similar MIN/MAX specialties?

However, I noticed, like Jerome, that MathML still lacks the following
fundamental set constructs:

   - empty set    (though Jerome gave a possible representation, 
     MathML would need to explicitly specify that it has this meaning,
     in particular since it would be illegal in the scheme above!)

   - powerset of a set  (could be implemented as {true,false}^set,
     that is using <power type="set"/>, but this notation is usually
     used to denote functions from one set to another, which makes the
     above representation only equivalent to, but not identical to, 
     the powerset notion).

   - Cartesian products and powers of sets
     (though a <times type="set"/> and <power type="set"/> could be used
     to implement this and to distinguish these products from the more
     common(?) use of multiplication of sets as the set of all products
     of pairs of elements of the sets, which would be represented by
     having a <times type="integer"/>, say, applied to two sets.

   - n-tuples (as opposed to vectors).

[Or did I miss something?]

BTW: is the type='...' attribute allowed to have values 'logical or
truth-value or boolean' or 'set'?  

These are fundamental, and should probably be treated this way -- it
should be simple to denote R^3, say, in a K-12 physics setting ;-)

  -- Andreas
Received on Tuesday, 29 February 2000 15:58:50 UTC

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