Talk:Cantor's first set theory article/Archive 1: Difference between revisions

Revision as of 13:09, 24 January 2010

Revision as of 21:34, 24 January 2010

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* In the paragraph beginning "The constructive nature of Cantor's work is most easily demonstrated by using it to construct an irrational number. " — isn't this using the diagonal method rather than the method of Cantor's first proof? Why not make an example that uses the method of the first proof.

I'll read through the article again today to copyedit again. &mdash;&nbsp;Carl <small>([[User:CBM|CBM]]&nbsp;·&nbsp;[[User talk:CBM|talk]])</small> 13:09, 24 January 2010 (UTC)

Thank you very much for your feedback:

* Concerning the relationship between Cantor's proof and the Baire category theorem: I regard the current article as mostly historical and Baire proved his theorem in 1899. Also, the versions of the Baire category theorem as stated at [[Baire category theorem]] require some form of the axiom of choice, which Cantor's methods do not need. So I suspect you are talking about a weaker form of the Baire category theorem. Perhaps a note could be added about the relationship between Cantor's 1874 method and the proof of the Baire category theorem if a source could be located.

* Sorry, I left out some references. I have added references to the locations in Gray 1994 where the computer program times are mentioned. (The sub-exponential time is at bottom p. 822 - top p. 823.)

* The diagonal method was used because it is simpler and the idea was just to demonstrate the constructive nature of Cantor's work. In this section, both of Cantor's methods are mentioned so I felt free to use the simplest method. Using Cantor's 1874 method gives the intervals [1/3, 1/2], [2/5, 3/7], [7/17, 5/12], … or in decimals [.33…, .50…], [.400…, 428…], [.4117…, .4166…], … It seems to me that the number generated by the diagonal method is more easily seen to be irrational than the number generated by the 1874 method. I'd like some feedback from other readers before changing methods. Of course, both methods could be illustrated.

* As for the class rating, I'll let the experts on class ratings discuss this. By the way, could you give me a Wiki reference to the definitions of each rating?

----[[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 21:34, 24 January 2010 (UTC)