tag:blogger.com,1999:blog-11788780.post1140577497253122655..comments2023-12-29T13:22:33.104-08:00Comments on JJinuxLand: SICP: Broken Mathjjinuxhttp://www.blogger.com/profile/03270879497119114175noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-11788780.post-41904011952072084962008-07-21T07:13:00.000-07:002008-07-21T07:13:00.000-07:00There is quite a theory about divergent series. H...There is quite a theory about divergent series. Have you found http://en.wikipedia.org/wiki/Divergent_series<BR/>where they give a bibliography, including a book by G. H. Hardy.<BR/><BR/>I think this particular sum is due to Euler.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-11788780.post-20758879632772966352008-07-19T16:13:00.000-07:002008-07-19T16:13:00.000-07:00> A nice one was found by GaussAh, yes, I know ...> A nice one was found by Gauss<BR/><BR/>Ah, yes, I know that story. The funny is when I showed my wife this "trick", she came up with the same story ;) So let me see:<BR/><BR/>n = infinity<BR/>(infinity (infinity - 1)) / 2 = infinity<BR/><BR/>(But note, it's the same "kind" of infinity, since there's a 1-1 mapping between the two.)jjinuxhttps://www.blogger.com/profile/03270879497119114175noreply@blogger.comtag:blogger.com,1999:blog-11788780.post-71736164321955621262008-07-19T16:11:00.000-07:002008-07-19T16:11:00.000-07:00> Although, if you write a C program to evaluat...> Although, if you write a C program to evaluate that sum using signed integers, it does converge to -1. :)<BR/><BR/>Haha, I thought of that too ;)<BR/><BR/>> Why do you call it a trick?<BR/><BR/>I didn't know what else to call it ;)jjinuxhttps://www.blogger.com/profile/03270879497119114175noreply@blogger.comtag:blogger.com,1999:blog-11788780.post-60363480200875280112008-07-19T16:10:00.000-07:002008-07-19T16:10:00.000-07:00A nice one was found by Gauss (it is said to, be m...A nice one was found by Gauss (it is said to, be maybe that's a legend...) when he was a child and asked to find this (finite) sum :<BR/> <BR/>Sn = 1 + 2 + 3 + ... + n<BR/><BR/>Gauss started by writing the numbers like this :<BR/> <BR/>Sn = 1 2 3 4 5 ... n<BR/><BR/>then in reversed order :<BR/>Sn = n n-1 n-2 2 1<BR/><BR/>What's the point ? He could now add each column and see that they all give n+1:<BR/><BR/>2*Sn = n+1 n+1 n+1 ... n+1<BR/><BR/>As with have n equal terms, 2*Sn is easily computed :<BR/>2*Sn = = n*(n+1)<BR/><BR/>So, Sn = n*(n+1)/2<BR/><BR/>Nice no ?!kibhttps://www.blogger.com/profile/02475335739134506765noreply@blogger.comtag:blogger.com,1999:blog-11788780.post-1561055452619508072008-07-19T15:54:00.000-07:002008-07-19T15:54:00.000-07:00Why do you call it a trick? Seems more like an ant...Why do you call it a trick? Seems more like an anti-trick to me, if anything. As in, no, really, don't try this at home or anywhere else.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-11788780.post-40069891508239242432008-07-19T15:46:00.000-07:002008-07-19T15:46:00.000-07:00Although, if you write a C program to evaluate tha...Although, if you write a C program to evaluate that sum using signed integers, it does converge to -1. :)stanhttps://www.blogger.com/profile/08688052715877131030noreply@blogger.comtag:blogger.com,1999:blog-11788780.post-74957444659002946822008-07-19T15:18:00.000-07:002008-07-19T15:18:00.000-07:00Funny post,Sussman is right, we have to be very ca...Funny post,<BR/><BR/>Sussman is right, we have to be very careful when handling limits.<BR/><BR/>But for this one, it seems rather natural that v will not be an integer.kibhttps://www.blogger.com/profile/02475335739134506765noreply@blogger.com