Kjetil et al, Unlike finite sums, infinite sums are not commutative. To have commutativity, one must have absolute summability, that is, the sum of the absolute values of the terms must be finite. If one has absolute summability, the infinite sum exists and is unique. This sum is not absolutely summable and thus undefined. If one does not require commutativity, then the order of the summation must be specified. The order is often implicitly assumed to be the order of the integers. The sum of the negative integers is negative infinity, the sum of the positive integers is infinity, and the sum of these two sums is undefined. However, Riemann's rearrangement theorem shows that the terms can be re-ordered to yield any sum whatsoever. In particular, if one creates pairs of terms consisting of a positive integer and its negative, then the infinite sum is zero. So the unique sum is undefined; otherwise the sum depends on the order of addition. Joe
David Winsemius <dwinsem...@comcast.net> Sent by: r-help-boun...@r-project.org 02/15/2011 09:17 AM To Kjetil Halvorsen <kjetilbrinchmannhalvor...@gmail.com> cc r-help@r-project.org, Maithula Chandrashekhar <m.chandrashekhar1...@gmail.com> Subject Re: [R] A Math question On Feb 14, 2011, at 7:33 PM, Kjetil Halvorsen wrote: > or even better: > > http://mathoverflow.net/ I beg to differ. That is designated in its FAQ as expecting "research level questions", while the forum I offered is labeled as "Welcome to Q&A for people studying math at any level and professionals in related fields". I don't think the proffered question could be considered "research level". > > On Sun, Feb 13, 2011 at 8:02 PM, David Winsemius <dwinsem...@comcast.net > > wrote: >> >> On Feb 13, 2011, at 4:47 PM, Maithula Chandrashekhar wrote: >> >>> Dear all, I admit this is not anything to do R and even with >>> Statistics perhaps. Strictly speaking this is a math related >>> question. >>> However I have some reasonable feeling that experts here would >>> come up >>> with some elegant suggestion to my question. >>> >>> Here my question is: What is sum of all Integers? I somewhere heard >>> that it is Zero as positive and negative integers will just cancel >>> each other out. However want to know is it correct? >> >> There are more appropriate places to pose such questions: >> http://math.stackexchange.com/ >> David Winsemius, MD West Hartford, CT ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
