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Tue Jan 28 00:16:04 PST 2003

I don't want to get into a mathematical discussion beyond my limited
expertise, but it has been known for 70 (or 40) years that there are
sensible math statements which are neither true nor false but in
fact undecidable.  For example, using the usual axioms mathematicians
can't tell you how many numbers there are.  Ok, this may not keep you from
sleeping at night, but even a relatively simple thing like a rigorous
discussion of what an integer actually is might give you nightmares (e.g.,
http://mcraefamily.com/MathHelp/BasicSetConstruction.htm) and the correct
definition of what a curve is or the area of a plane figure or what's
special about the number 163 - to say it's harrowing is an understatement.

This reminds me I was going to go reread Vlad and Cawti's argument about
bootstrapping in Yendi and try to figure out Brust's position.

- Philip

On Mon, 27 Jan 2003 Gaertk at aol.com wrote:

> In a message dated 1/27/2003 4:52:24 PM Eastern Standard
> Time, Philip Hart <philiph at SLAC.Stanford.EDU> writes:
> > Not to be pedantic, but can you teach any math to anyone
> > short of a very sharp college student without fudging?  I
> > doubled in physics and math at Cornell but my intro to real
> > analysis (the "baby" version) was unpleasant.
> Hmm.  I don't see any need of fudging for arithmatic, most
> algebra (maybe excluding exponents), and some geometry.  If
> the students can be taught limits, much of differential
> calculus can be easily derived.  Trig might be a problem,
> though (I don't know the basis for that).
> --KG