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| ``Re: Cartesian product''
by drini on 2004-09-30 14:40:45 |
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It is used here because that is the standard mathematical notation. Also, it's similarr to using Sigma (\sum) to denote addition instead a big cross. After all.. you're "multiplying" spaces, so the usual notation from calculus is kind of sensical.
The product symbol (\product (the large pi)) dates back to Descartes (http://members.aol.com/jeff570/operation.html)
And on your comment, I've NEVER seen any textbook nor teacher in university that ever uses a large X symbol to denote product (just as I've not seen used a large + symbol instead of sum.
Incidentally, I don't think \bigtimes and \bigplus are standard latex symbols (at least I don't recall). Indeed, there are \bigotimes and \bigoplus, but they carry some meaning usually different than cartesian product or sum (they being usually tensor product and direct sum)
I hope this clears the doubt on why \product is used to denote arbitrary products of things instead of a large X
It's how it's been done in mathematics for long long time
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f |
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