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Re: Denoting a Cartesian Product

• To: mathgroup at smc.vnet.net
• Subject: [mg91002] Re: [mg90937] Denoting a Cartesian Product
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 2 Aug 2008 03:28:21 -0400 (EDT)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200807300753.DAA17781@smc.vnet.net>
• Reply-to: murray at math.umass.edu

Ordinarily, the n-fold cartesian product of a single set B would be 
denoted B^n  (with a superscript)!

If you want the cartesian product of a family of sets B_1, B_2, ..., 
B_n, then the usual notation would be the one you get from the Basic 
Math Input palette, with a large pi-type product sign.

Unfortunately, that's a rotten notation -- and this has nothing to do 
with Mathematica per se, but with mathematicians and, more likely, 
typographers.  The "obvious" thing to do is what you almost suggest, 
that is, to have a large Times sign instead of that large pi-like 
product sign.  But one cannot simply magnify the small Times sign, since 
the proportions will be wrong: the width needs to have a smaller ratio 
to the height after the magnification.

Bruce Colletti wrote:
> Re Mathematica 6.0.3 under WinXP.
> 
> In a text cell, how would I denote the n-fold Cartesian Product of set B (without saying B x B x ... x B)?
> 
> I've used the basic input palette's summation button, replacing sigma by X, but the look isn't right (by setting ScriptLevel to 0, indexing appears over and under the X).  Am hoping there's an easy way.
> 
> Thanks.
> 
> Bruce
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305