Dieudonne on Dedekind

martdowd at aol.com martdowd at aol.com
Wed Aug 11 12:52:12 EDT 2021

Tim Chow wrote:

he wants 
undergrads to take for granted (and in particular, not worry about 
proving) the existence of an ordered field with the least upper bound 
property.  That is, he's not arguing for this proof of existence versus 
that proof of existence.  Rather, on this view, undergrads need not worry 
about the existence question at all.
 I'ld like to recommend chapter 8 of my book   A Beginner's Guide to Modern Set Theory   https://www.researchgate.net/publication/337334150This uses informal set theory to construct the reals as an orderedfield using Dedekind cuts.  First, the integers are constructed fromthe non-negative integers, and then the rationals are constructedfrom the integers.  In my mathematical education, this was a classicalmethod, and I've tried to write it up for advanced high-schoolstudents.  Three chapters later, the axioms of ZFC are given.

 I came in second in a high-school math talk contest once.  I talked aboutthe complex logarithm.  The winner talked about Dedekind cuts.
Martin Dowd
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