I just found out that the sum of 1+2+3+... is -1/12. !?! Crazy. Not really. Google on divergent series or Euler summation. The result explains why bosonic string theory must operate only in 26 dimensions! It would then appear that ... -3 - 2 - 1 + 0 +1 +2 +3 + ... is zero.
peter dalgaard <[email protected]> Sent by: [email protected] 02/15/2011 11:53 AM To David Winsemius <[email protected]> cc [email protected], Kjetil Halvorsen <[email protected]>, Maithula Chandrashekhar <[email protected]> Subject Re: [R] A Math question On Feb 15, 2011, at 15:17 , David Winsemius wrote: > > 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". Yep. As for the stats contents, we do actually touch upon the question in basic probability. This is the reason that sums over infinite index sets are only defined if the corresponding sum of the absolute value is finite: Otherwise the result depends on the order of summation. (Think 0+1+2+(-1)+3+4+(-2)+5+6+(-3)+....) > >> >> On Sun, Feb 13, 2011 at 8:02 PM, David Winsemius <[email protected]> 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 > > ______________________________________________ > [email protected] 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. -- Peter Dalgaard Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: [email protected] Priv: [email protected] ______________________________________________ [email protected] 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]] ______________________________________________ [email protected] 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.
