Favorite NON-fiction ?

Michael Barr barr at barrs.org
Sun Feb 2 04:31:12 PST 2003

> In college, I had the fortune to take a math class that showed how
> to derive the real numbers and modern mathematics from very limited
> set theory-- just a handful of basic postulates and lots of logic
> were all it took to get to arithmetic, calculus, and beyond.
> At that point, I finally understood why *every* year in grade
> school, math started out with a week of set theory and then
> dropped the topic like a hot potato:  they were trying to pass on
> this beautiful vision, but were utterly failing to do so.
> -- 
> %% Max Rible % slothman at amurgsval.org % www.amurgsval.org/~slothman/ %%
> %% "Before enlightenment:  sharpen claws, catch mice.                %%
> %%  After enlightenment:  sharpen claws, catch mice."                %%

I'm glad you enjoyed it, but it really is a waste of time to study set
theory to do calculus, since the nature of the actual sets involved is
utterly irrelevant.  What you need is certain properties of real numbers
(the technical properties are summarized by "complete archimedean ordered
field", which I will not try to explain here) and that is all you need
since that characterizes the real numbers (up to unique isomorphism).

Having elementary school teachers trying to teach set theory is like
asking your HS physics teacher try to teach string theory.  To paraphrase
snoopy, they are trying to do new math with old math minds.  I saw my own
children's teachers making absurd attempts and decided that they were
doing more harm than good.  To introduce the "New Math" without a thorough
retraining of the teachers (which was probably impossible anyway, once
they had been through schools of education) was folly.