Talk:Riemann series theorem

message: Hi! I was just poking through some articles, and after looking at "absolute convergence", I wound up here. I didn't find a worked example of how a conditionally convergent series can actually be re-arranged to yield two different sums in either place. I think such an example would be helpful to the general reader. I also think this article should mention earlier results of Cauchy and Dirichlet.  DavidCBryant 13:51, 23 January 2007 (UTC)
thread_title: Long on theory, short on specifics

message: criticism for Riemann's theorem
on a sum of conditionaly convergent series
(pdf,eng,26KB)
http://alexander-conon.narod.ru/science/crte.pdf
comment on "criticism for Riemann's theorem
on a sum of conditionaly convergent series"
(pdf,eng,26KB)
http://alexander-conon.narod.ru/science/crte-c.pdf
82.151.112.75 (talk) 00:10, 25 June 2008 (UTC)
thread_title:  Add ? 

message: I added references that discuss the Riemann-series theorem and its applications. Some of these also discuss infinite-dimensional versions (e.g. problem 28 of the Scottish Book) and links to probability theory (e.g. exchangeability, weak exchangeability, etc.). Thanks, Kiefer.Wolfowitz (talk) 17:53, 11 October 2010 (UTC)
thread_title:  References 

message: Dini, an italian mathematician. 62.18.122.161 (talk) 14:35, 1 December 2021 (UTC)
replies: text: Only in italian wikipedia. https://it.wikipedia.org/wiki/Teorema_di_Riemann-Dini 2A00:1370:8184:2478:6C69:76C3:10A3:2E5B (talk) 09:58, 5 July 2022 (UTC)
thread_title:  Isn't this theorem called "rienmann-dini"? 

message: Does not this theorem mean conditionally divergent series can be rearranged to converge, but not absolutely divergent? Obviously the defintion of absolute is different. Valery Zapolodov (talk) 04:34, 14 January 2022 (UTC)
replies: text: Ha, found it! https://math.stackexchange.com/a/1221227/756502 Valery Zapolodov (talk) 04:38, 14 January 2022 (UTC)
replies: text:  Yes of course.  But this is unimportant and certainly should not be mentioned as part of the statement of the theorem (which it is not).  And it shouldn't be in the article at all without a reliable source (for reasons on due weight). --JBL (talk) 13:11, 14 January 2022 (UTC)
thread_title:  Conditional divergence? 

message: They are only ever published in Polish. It was hard.
The first paper was catalogued in French, but it was only published in Polish, in  Sprawozdania z posiedzen Towarzystwa Naukowego Warszawskiego [Meeting reports of the Warsaw Scientific Society]. It is recorded here in page 129 of International Catalogue of Scientific Literature, 1901-1914 (1912 May, volume A Mathematics).
The title is "Przyczynek do teoryi szeregów rozbieznych", though sometimes the "teoryi" is misspelled as "teorii". I found an online version here . It was "Komunikat zgłoszony dn. 30 grudnia 1909 r." ["Communicated on 1909-12-30"].
The second paper is  "Uwaga do twierdzenia Riemanna o szeregach warunkowo zbieżnych" pulished in Prace Matematyczno-Fizyczne (in Polish). 21 (1): 17–20. It comes with a French title [Remarque sur le théorème de Riemann relatif aux séries semiconvergentes], though it wasn't published in French. pony in a strange land (talk) 17:16, 31 December 2022 (UTC)
thread_title:  found Sierpinski's original papers