[FOM] Wildberger on Foundations
aa at tau.ac.il
Tue Jul 17 07:05:39 EDT 2012
On Wed, Jul 11, 2012 at 12:51:02PM -0400, joeshipman at aol.com wrote:
> In his discussion with me, he asks for examples of texts where the
> modern framework of Analysis is developed completely rigorously from
> first principles.
> Can anyone suggest some source books that might satisfy his request?
Here are two books which were used as the main textbooks in undergrduate
courses I took about 40 years ago in Tel-Aviv university, and come
close to this ideal:
G. M. Fikhtengol'ts: The fundamentals of Mathematical Analysis
This is the book from which I have learned Analysis. It
starts with a rigorous introduction of the real numbers as
Dedekind cuts, and continue to provide rigorous definitions and proofs
in both of its two comprehensive volumes. It does not provide a list of
"basic principles", though.
J. Dugundji: Topology
This book is not a book in analysis. However, it is relevant here
because it is almost fully self-contained. It starts from elementary
set theorys, and it even provides a full list of axioms (GB in an
And I should mention of course also Feferman's classic book on the
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