tag:blogger.com,1999:blog-5592542.post5725706747757377795..comments2022-12-05T09:54:58.782-08:00Comments on Rondam Ramblings: No, the sum of all the positive integers is not -1/12Ronhttp://www.blogger.com/profile/11752242624438232184noreply@blogger.comBlogger16125tag:blogger.com,1999:blog-5592542.post-72799185126696331042014-02-26T21:26:10.613-08:002014-02-26T21:26:10.613-08:00I don't either agree with the two British math...I don't either agree with the two British mathematicians. I think their theory is as strange as wrong. I guess Ron's analyses are great and clear, mainly that part of sum of non-converging infinite sums. <br />I've got something else to prove their theory isn't correct.<br /><br />Let S1 = 1 + 1 + 1 + 1 + 1 + ...<br />This sum logically goes to infinit. <br />Let S2 = 1 + 2 + 3 + Viníciushttps://www.blogger.com/profile/03546852906985989849noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-28419227061265331432014-02-18T04:51:31.251-08:002014-02-18T04:51:31.251-08:00What possible harm can it do if a few (million?) p...What possible harm can it do if a few (million?) people come to believe that the sum of all the positive integers is a small negative rational number? Ralph Dratmanhttps://www.blogger.com/profile/00426433134164984467noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-78291438906300040432014-01-21T12:42:23.597-08:002014-01-21T12:42:23.597-08:00Sorry, let me redo that offset series addition:
...Sorry, let me redo that offset series addition:<br /><br /><br />1 + 2 + 3 + 4 + 5 + ... "= -1/12"<br /> ......-2 - 4 - 6 - 8 - ... "= 1/6"<br />---------------------------------------------------<br />1..........-1 - 2 - 3 - .... = 1 1/12 OR 1/12?<br /><br />Sliding the -2x of the original series over more and more creates ever larger discrepancies. It is Neil Bateshttps://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-39428458377788968332014-01-21T12:38:23.558-08:002014-01-21T12:38:23.558-08:00Indeed, it does not. I have found a direct contrad...Indeed, it does not. I have found a direct contradiction in the treating of the infinite sum of positive integers (1 + 2 + 3 + 4 + 5 + ...) = -1/12. Yes I know, it can be related to that number by the zeta function etc. but the concept is not algebraically consistent. I don't just mean regarding rearranging associative parentheses either. The infamous proof in the circulating Youtube makes Neil Bateshttps://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-442785757706171002014-01-19T04:05:15.021-08:002014-01-19T04:05:15.021-08:00Hmmm,
this"wrong" manipulations of diver...Hmmm,<br />this"wrong" manipulations of diverging series remind me of complete induction. <br />Is there some connection? <br />GeorgGeorghttps://www.blogger.com/profile/02538391164351204407noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-23871240979329342582014-01-18T22:54:28.991-08:002014-01-18T22:54:28.991-08:00I think the author only watched one of the 2 video...I think the author only watched one of the 2 videos of numberphile. tensaix2jhttps://www.blogger.com/profile/03967406630916930341noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-537587419677238082014-01-18T20:02:54.438-08:002014-01-18T20:02:54.438-08:00Finally someone... Thanks!Finally someone... Thanks!Unknownhttps://www.blogger.com/profile/00644799052084808735noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-64385816454543428352014-01-18T08:10:12.251-08:002014-01-18T08:10:12.251-08:00They actually do mention riemann zeta functions
...They actually do mention riemann zeta functions <br /><br />https://www.youtube.com/watch?v=w-I6XTVZXww&t=1m3s<br /><br />and they have another video explaining the correct proof using them.<br /><br />https://www.youtube.com/watch?v=E-d9mgo8FGkvertical rockhttps://www.blogger.com/profile/16039370973676069514noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-4919222045460134162014-01-18T07:26:24.197-08:002014-01-18T07:26:24.197-08:00Made a mistake :P
2S''=1+1/2
S=3/4Made a mistake :P<br /><br />2S''=1+1/2 <br />S=3/4<br />Nuno Joséhttps://www.blogger.com/profile/02108678810340854904noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-63402445641405677072014-01-18T07:23:16.636-08:002014-01-18T07:23:16.636-08:00We could also assume that 2S'' is realy 1+...We could also assume that 2S'' is realy 1+1/2 so = 3/4<br /><br />So:<br /><br />S = -1/4<br /><br />So -1/12=-1/4Nuno Joséhttps://www.blogger.com/profile/02108678810340854904noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-61077207001135401192014-01-18T07:16:06.439-08:002014-01-18T07:16:06.439-08:00Jon, I think Ron's problem is not about infini...Jon, I think Ron's problem is not about infinite series themselves. The problem is about the care and rigor one has to maintain when doing mathematics properly. The video failed in this regard.<br /><br />Literate people know what are "+" and "=". We use them every day. But the guys in the video overloaded "=" without even giving the name to it. It's not &ashhttps://www.blogger.com/profile/06881159517883261190noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-33571756833391148112014-01-18T01:37:55.192-08:002014-01-18T01:37:55.192-08:00"A grave disservice to numerical literacy&quo..."A grave disservice to numerical literacy" Good grief, do you think you could sound any more absurdly pompous if you tried? Most people's numerical literacy doesn't extend past high school mathematics, and doesn't need to. They certainly won't be harmed by having a confused understanding of infinite series. Given the amount of debate this video has generated, I'm notJon Rimmerhttps://www.blogger.com/profile/07587503998121686945noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-45660890162646073622014-01-17T22:07:35.062-08:002014-01-17T22:07:35.062-08:00I've seen the video and the addendum and resea...I've seen the video and the addendum and researched this on Wikipedia and found that it doesn't work on divergent series pretty quickly:<br />http://en.wikipedia.org/wiki/Reimann_zeta_function<br /><br />Pretty shoddy research from Slate.<br /><br />However, I did find it interesting that Numberphile mentioned that -1/12 shows up in quantum field theory fairly regularly (Casimir effect, Corbyhttps://www.blogger.com/profile/02160776611694374837noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-7300790537513030522014-01-17T18:05:11.412-08:002014-01-17T18:05:11.412-08:00Your "real math" link has another intere...Your "real math" link has another interesting example. S3 (1+1+1...) "sums" to -1/2. S (1+2+3+4...) "sums" to -1/12. Now add S3+S together. Term by term gets us 2+3+4+5... Adding the "sums" gets us -1/2 + -1/12 = -7/12. But, alternatively, you can just start with S (1+2+3+4...) = -1/12, and subtract 1 from both sides, to get (0+2+3+4...) = -13/12. Don Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-16232414589916496122014-01-17T17:55:35.154-08:002014-01-17T17:55:35.154-08:00My friend, Ray Sidney, with a PhD in mathematics f...My friend, Ray Sidney, with a PhD in mathematics from MIT explained away this nonsense rather succinctly.<br /><br />infinity + 7 = infinity<br /><br />If you minus infinity from both sides, you can tell the world 7 = 0!Jeremy Stieglitzhttps://www.blogger.com/profile/09309736577662310839noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-77283717141950814712014-01-17T17:30:46.153-08:002014-01-17T17:30:46.153-08:00This comment has been removed by the author.Chrishttps://www.blogger.com/profile/09981706309245901560noreply@blogger.com