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Topic: Is "motivation" in mathematics a fairy tale?
Replies: 93   Last Post: Apr 11, 2014 2:07 PM

 Messages: [ Previous | Next ]
 Paul Posts: 780 Registered: 7/12/10
Re: Is "motivation" in mathematics a fairy tale?
Posted: Apr 8, 2014 4:10 AM

On Monday, April 7, 2014 8:44:14 PM UTC+1, dull...@sprynet.com wrote:
...> HAve you got any idea what Cantor was working on, that _forced_ him to
>
> study infinite ordinals? I didn't think so. It was a problem in
>
> Fourier series!
>
>
>
> (Specifically, which sets E have the property that if a trig series
>
> converges to 0 on the complement of E then the coefficients
>
> vanish...)
>
>

...

From a few minutes casual googling, it seems that Cantor proved using transfinite induction (the origins for Cantor's development of set theory) that finite sets E have the above property. Others than proved that countable sets E have the same property.

Apparently, not all sets of Lebesgue measure 0 are sets of uniqueness. (A set of uniqueness is a set of the type described by E).

So this is some interesting classical mathematics. As you may know, from other threads, I like to read proofs of great classical theorems and then ask sci.math when I need help.

Many of my questions go unanswered (for example, when I got stuck on Szemeredi's proof of his theorem about subsets of the natural numbers of positive upper density).

I'm wondering what I can do, to improve my success at getting my questions answered. You (David Ullrich) made the excellent point that it's a good idea to learn a lot of the underlying theory first by doing related exercises. Maybe, that's really the only way to make progress, I don't know. With the Szemeredi proof, the original 1975 proof is so totally elementary that it's hard to see how doing other exercises can help or what those exercises would be.

A digression, I know, but perhaps that's forgivable.

Paul Epstein

Date Subject Author
4/6/14 Victor Porton
4/6/14 ross.finlayson@gmail.com
4/6/14 magidin@math.berkeley.edu
4/6/14 Port563
4/7/14 mueckenh@rz.fh-augsburg.de
4/7/14 Virgil
4/7/14 magidin@math.berkeley.edu
4/7/14 mueckenh@rz.fh-augsburg.de
4/7/14 magidin@math.berkeley.edu
4/7/14 Virgil
4/7/14 David C. Ullrich
4/7/14 mueckenh@rz.fh-augsburg.de
4/7/14 Virgil
4/7/14 Peter Percival
4/7/14 ross.finlayson@gmail.com
4/8/14 mueckenh@rz.fh-augsburg.de
4/10/14 David C. Ullrich
4/8/14 Paul
4/8/14 Peter Percival
4/8/14 Port563
4/10/14 David C. Ullrich
4/10/14 David C. Ullrich
4/7/14 magidin@math.berkeley.edu
4/7/14 mueckenh@rz.fh-augsburg.de
4/7/14 Arturo Magidin
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 Virgil
4/8/14 magidin@math.berkeley.edu
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 magidin@math.berkeley.edu
4/8/14 magidin@math.berkeley.edu
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 magidin@math.berkeley.edu
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 Virgil
4/8/14 Virgil
4/8/14 Virgil
4/8/14 Virgil
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 Virgil
4/8/14 Port563
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 Port563
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 Port563
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 Virgil
4/9/14 mueckenh@rz.fh-augsburg.de
4/9/14 Port563
4/9/14 mueckenh@rz.fh-augsburg.de
4/9/14 Virgil
4/10/14 mueckenh@rz.fh-augsburg.de
4/10/14 Virgil
4/10/14 mueckenh@rz.fh-augsburg.de
4/10/14 Virgil
4/10/14 mueckenh@rz.fh-augsburg.de
4/10/14 Virgil
4/9/14 Virgil
4/9/14 Virgil
4/10/14 Virgil
4/10/14 Virgil
4/10/14 Virgil
4/10/14 Virgil
4/10/14 Virgil
4/8/14 Virgil
4/8/14 magidin@math.berkeley.edu
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 Virgil
4/8/14 magidin@math.berkeley.edu
4/7/14 Arturo Magidin
4/7/14 Arturo Magidin
4/7/14 Virgil
4/7/14 magidin@math.berkeley.edu
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 Virgil
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 Virgil
4/8/14 FredJeffries@gmail.com
4/8/14 mueckenh@rz.fh-augsburg.de
4/8/14 Virgil
4/6/14 William Elliot
4/7/14 Cate
4/7/14 Brian Q. Hutchings
4/7/14 Port563
4/8/14 Brian Q. Hutchings
4/9/14 Brian Q. Hutchings
4/11/14 Brian Q. Hutchings
4/7/14 David C. Ullrich