[FOM] Wildberger on Foundations

[Craig Smorynski]

All I know about asteroids is what I learned from Armageddon and Deep Impact. But I do mention that Prof. M wrote books on both subjects.

I think my book will be moderately entertaining and informative, if a bit less opinionated than my books on Formalism and Probability. The binomial theorem just didn't seem to lend itself to pontificating.

On Jul 19, 2012, at 9:01 PM, Joe Shipman wrote:

> I look forward to your upcoming Treatise on the Binomial Theorem; should we anticipate a sequel on the Dynamics of an Asteroid? -- JS
> 
> Sent from my iPhone
> 
> On Jul 19, 2012, at 1:29 PM, Craig Smorynski <smorynski at sbcglobal.net> wrote:
> 
>> When I was a student there was a very rigorous calculus textbook by Johnson and Kiokemeister. More to my liking were the pair
>> Calculus with Analytic Geometry
>> Vector Calculus and Differential Equations
>> by Albert G. Fadell, both published by van Nostrand (1964 and 1968, respectively).
>> 
>> On the matter of the foundations of the real number line, I might note that I give an exhaustive treatment in my Adventures in Formalism, discussing treatments by Bolzano, Weierstrass (not quite so exhaustive), Dedekind (overly detailed), and Heine-Cantor-Meray using Cauchy sequences. (End of advertisement.)
>> 
>> Also by way of an advertisement, I might mention my upcoming A Treatise on the Binomial Theorem in which I discuss the development of rigour as it was needed to provide a genuine proof of Newton's binomial theorem, first with complete rigour by Bolzano and then Cauchy and finally almost completely rigorously by Abel.
>> 
>> On Jul 17, 2012, at 6:05 AM, Arnon Avron wrote:
>> 
>>> 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 
>>>  informal form).
>>> 
>>> And I should mention of course also Feferman's classic book on the
>>> number systems.
>>> 
>>> 
>>> Arnon Avron
>>> 
>>> 
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>> 
>> Craig
>> 
>> 
>> 
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Craig



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