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Re: Re:apples and oranges



Date: Fri, 30 Oct 1998 21:00:27 -0600 (CST)
From: rgrandy@ruf.rice.edu (Richard Grandy)

Perhaps you could give an example of what other choices we might have made
in inventing the negative or irrational numbers.

For "other" irrationals, look up p-adic numbers. Basically, the
irrationals are obtained by completing the rationals. It turns
out that there are many choices for the completion process, and
the usual plus the p-adics represents a countable infinity of them
that have proven useful in number theory.
If p-adics turn out to be too tame, try real number objects in an
elementary topos. This changes *everything*.

---------------------------------------------
Phil Parker pparker@twsuvm.uc.twsu.edu
Random quote for this second:
ADA, n.:
Something you need only know the name of to be an Expert in
Computing. Useful in sentences like, "We had better
develop an ADA awareness."