tag:blogger.com,1999:blog-11295132.post115582909486668139..comments2014-10-20T08:43:52.658-07:00Comments on A Neighborhood of Infinity: What can we measure? Part IIDan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-11295132.post-1156266366012268052006-08-22T10:06:00.000-07:002006-08-22T10:06:00.000-07:00kim-ee,In twos-complements, 111...=-1. The series ...kim-ee,<BR/><BR/>In twos-complements, 111...=-1. The series converges in the 2-adic metric. But the next day a physicist might use the 3-adic metric, and the next day they might sum a^n where a isn't an integer and so on.<BR/><BR/>I know the Koblitz book. The proof of the von Staudt-Clausen Theorem in it is very beautiful.<BR/><BR/>BTW The guy Baez credits for the wacky alternative way to sum 1+2+3+... is in fact me :-)sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1156225940505118662006-08-21T22:52:00.000-07:002006-08-21T22:52:00.000-07:001+2+4+8+... = 1111111... in binary = -1 in so-call...1+2+4+8+... = 1111111... in binary = -1 in so-called twos-complement arithmetic. Seen this way, the computation isn't so bizarre.<BR/><BR/>IIRC an undergrad textbook by Koblitz goes into the basics of the p-adics and their connection with zeta functions.<BR/><BR/>Thanks for the <A HREF="http://math.ucr.edu/home/baez/week126.html" REL="nofollow">Baez link</A>. I didn't know there was a way of showing 1+2+3+... = -1/12 without appealing to the zeta functional equation, Γ(1/2) = √π, and whatnot.Kim-Ee Yeohhttp://www.blogger.com/profile/03063816445379881605noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1156177908593040502006-08-21T09:31:00.000-07:002006-08-21T09:31:00.000-07:00alpheccar,I guess you're talking about this stuff....alpheccar,<BR/><BR/>I guess you're talking about <A HREF="http://arxiv.org/abs/hep-th/9808042" REL="nofollow">this</A> stuff. That looks really intriguing. Much of it seems over my head but I've a hunch there are some parts that I night be able to make sense of.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1156176151165003862006-08-21T09:02:00.000-07:002006-08-21T09:02:00.000-07:00This blog is too cool !I remember that Connes and ...This blog is too cool !<BR/><BR/>I remember that Connes and Co. wrote some articles about renormalisation where they used Hopf algebras. I never had time to read those articles.<BR/><BR/>So, the question is : is there a link between Euler characteristic and Hopf Algebras. I can't find anything about it.alpheccarhttp://www.blogger.com/profile/16135510633295968366noreply@blogger.com