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

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Paul

Posts: 474
Registered: 7/12/10
Re: Is "motivation" in mathematics a fairy tale?
Posted: Apr 8, 2014 4:10 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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...)
>
>

...

I had no idea about this either, and I find this side-topic far more interesting than the actual thread.

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
Read Is "motivation" in mathematics a fairy tale?
Victor Porton
4/6/14
Read Re: Is "motivation" in mathematics a fairy tale?
ross.finlayson@gmail.com
4/6/14
Read Re: Is "motivation" in mathematics a fairy tale?
magidin@math.berkeley.edu
4/6/14
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Port563
4/7/14
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mueckenh@rz.fh-augsburg.de
4/7/14
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Virgil
4/7/14
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magidin@math.berkeley.edu
4/7/14
Read Re: Is "motivation" in mathematics a fairy tale?
mueckenh@rz.fh-augsburg.de
4/7/14
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magidin@math.berkeley.edu
4/7/14
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Virgil
4/7/14
Read Re: Is "motivation" in mathematics a fairy tale?
David C. Ullrich
4/7/14
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mueckenh@rz.fh-augsburg.de
4/7/14
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Virgil
4/7/14
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Peter Percival
4/7/14
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ross.finlayson@gmail.com
4/8/14
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mueckenh@rz.fh-augsburg.de
4/10/14
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David C. Ullrich
4/8/14
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Paul
4/8/14
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Peter Percival
4/8/14
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Port563
4/10/14
Read Re: Is "motivation" in mathematics a fairy tale?
David C. Ullrich
4/10/14
Read Re: Is "motivation" in mathematics a fairy tale?
David C. Ullrich
4/7/14
Read Re: Is "motivation" in mathematics a fairy tale?
magidin@math.berkeley.edu
4/7/14
Read Re: Is "motivation" in mathematics a fairy tale?
mueckenh@rz.fh-augsburg.de
4/7/14
Read Re: Is "motivation" in mathematics a fairy tale?
Arturo Magidin
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
mueckenh@rz.fh-augsburg.de
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
Virgil
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
magidin@math.berkeley.edu
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
mueckenh@rz.fh-augsburg.de
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
magidin@math.berkeley.edu
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
magidin@math.berkeley.edu
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
mueckenh@rz.fh-augsburg.de
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
magidin@math.berkeley.edu
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
mueckenh@rz.fh-augsburg.de
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
Virgil
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
Virgil
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
Virgil
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
Virgil
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
mueckenh@rz.fh-augsburg.de
4/8/14
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Virgil
4/8/14
Read Re: Is "motivation" of mueckenh@rz.fh-augsburg.de a fit subject for sci.math?
Port563
4/8/14
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mueckenh@rz.fh-augsburg.de
4/8/14
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Port563
4/8/14
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mueckenh@rz.fh-augsburg.de
4/8/14
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Port563
4/8/14
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mueckenh@rz.fh-augsburg.de
4/8/14
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Virgil
4/9/14
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mueckenh@rz.fh-augsburg.de
4/9/14
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Port563
4/9/14
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mueckenh@rz.fh-augsburg.de
4/9/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/10/14
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mueckenh@rz.fh-augsburg.de
4/10/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/10/14
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mueckenh@rz.fh-augsburg.de
4/10/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/10/14
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mueckenh@rz.fh-augsburg.de
4/10/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/9/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/9/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/10/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/10/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/10/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/10/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/10/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/8/14
Read Re: Is "motivation" of muec...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/8/14
Read Re: Is "motivation" of muec...@rz.fh-augsburg.de a fit subject for sci.math?
magidin@math.berkeley.edu
4/8/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
mueckenh@rz.fh-augsburg.de
4/8/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
Virgil
4/8/14
Read Re: Is "motivation" of mue...@rz.fh-augsburg.de a fit subject for sci.math?
magidin@math.berkeley.edu
4/7/14
Read Re: Is "motivation" in mathematics a fairy tale?
Arturo Magidin
4/7/14
Read Re: Is "motivation" in mathematics a fairy tale?
Arturo Magidin
4/7/14
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Virgil
4/7/14
Read Re: Is "motivation" in mathematics a fairy tale?
magidin@math.berkeley.edu
4/8/14
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mueckenh@rz.fh-augsburg.de
4/8/14
Read Re: Is "motivation" in mathematics a fairy tale?
Virgil
4/8/14
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mueckenh@rz.fh-augsburg.de
4/8/14
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Virgil
4/8/14
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FredJeffries@gmail.com
4/8/14
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mueckenh@rz.fh-augsburg.de
4/8/14
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Virgil
4/6/14
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William Elliot
4/7/14
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Cate
4/7/14
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Brian Q. Hutchings
4/7/14
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Port563
4/8/14
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Brian Q. Hutchings
4/9/14
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Brian Q. Hutchings
4/11/14
Read Re: Is "motivation" in mathematics a fairy tale?
Brian Q. Hutchings
4/7/14
Read Re: Is "motivation" in mathematics a fairy tale?
David C. Ullrich

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