Dragaera

Philip Hart
philiph at SLAC.Stanford.EDU

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>>