tag:blogger.com,1999:blog-8155036766532593680.post2573129893771194211..comments2020-07-30T16:55:04.539-07:00Comments on Cantor on the Shore: The Real Meaning of To Infinity and Beyond!Vincenzo Dimontehttp://www.blogger.com/profile/18171790656280332547noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-8155036766532593680.post-25855519168066499372017-03-12T00:24:18.711-08:002017-03-12T00:24:18.711-08:00You may be able to do more than you think. But eve...You may be able to do more than you think. But even an infinite sequence of digits shows only an infinity of failures to define a real number precisely. To define an irrational number by fractions (= digits) is absolutely impossible.<br /><br />Regards, WMWMhttps://www.blogger.com/profile/15911521190071762395noreply@blogger.comtag:blogger.com,1999:blog-8155036766532593680.post-64104251599139840912017-02-03T17:23:04.060-08:002017-02-03T17:23:04.060-08:00"To infinity, and beyond" = "I can ..."To infinity, and beyond" = "I can do more than even I think I am capable of doing" This applies to mathematicians as well as the rest of us mere mortals :)BrĂ¼s NaGromhttps://www.blogger.com/profile/01483936810093085808noreply@blogger.comtag:blogger.com,1999:blog-8155036766532593680.post-44319294567425251242016-12-01T04:10:25.291-08:002016-12-01T04:10:25.291-08:00Set theory is imprecise. From the following three ...Set theory is imprecise. From the following three distinctions it recognizes only one, namely the first one: <br /><br />(1) <br />The union of the sequence of intervals [0, (n-1)/n] is [0, 1). It is the "set.theoretic" limit. <br />The *limit* of the sequence of intervals [0, (n-1)/n] is [0, 1]. This is the analytical limit obtained from lim((n-1)/n) = 1. <br /><br />(2) <br />The union of the sequence of finite initial segments of the sequence of natural numbers {1}, {1, 2}, {1, 2, 3}, ... has less then aleph_0 elements. This can easily be seen from the figure<br />1<br />1, 2<br />1, 2, 3<br />...<br />When shifting all finite rows into the first row, no row with aleph_0 numbers can be created because every row lacks aleph_0 numbers.<br />The *limit* of the sequence of finite initial segments of the sequence of natural numbers {1}, {1, 2}, {1, 2, 3}, ... has aleph_0 elements. <br /><br />(3) <br />A decimal representation (= series or sequence of partial sums like 3.1, 3.14, 3.141, ...) is never irrational. It has aleph_0 rational terms failing to be the limit.<br />The *limit* of a the sequence can be irrational. Alas it is not subject to the folklore version of Cantor's diagonal argument.<br /><br />Many defenders of set theory claim that when writing an infinite series like 0.999... automatically the limit 1 is meant by definition. But they do not claim that by the union over {1}, {1, 2}, {1, 2, 3}, ... also automatically the limit is meant. Here they believe that the union has aleph_0 elements. And all formal systems agree to this mistake. Therefore all this is imprecise. No mathematics.<br /><br />For more information see https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf<br /><br />Regards, WM<br />WMhttps://www.blogger.com/profile/15911521190071762395noreply@blogger.comtag:blogger.com,1999:blog-8155036766532593680.post-24132798408924206892016-04-19T18:25:30.981-07:002016-04-19T18:25:30.981-07:00Yes, this is likely a paraphrase of Kubrick, but t...Yes, this is likely a paraphrase of Kubrick, but the Macho Man Randy Savage actually said the phrase exactly as "To infinity and beyond" twice in a promo. Maybe the writer just liked some classic Rasslin'.Shawnhttps://www.blogger.com/profile/16023291533389012904noreply@blogger.comtag:blogger.com,1999:blog-8155036766532593680.post-83137519606961569552016-04-16T03:05:14.731-07:002016-04-16T03:05:14.731-07:00Ha ha, no, in the end I could find no Sanjay Gupta...Ha ha, no, in the end I could find no Sanjay Gupta in the department of mathematics. Maybe he was in another department, bu I felt that going around the campus asking for a guy I've read on the internet would have been embarassing for my host...Vincenzo Dimontehttps://www.blogger.com/profile/18171790656280332547noreply@blogger.comtag:blogger.com,1999:blog-8155036766532593680.post-59472847006244269502016-04-13T12:45:40.170-07:002016-04-13T12:45:40.170-07:00Did you meet Dr. Sanjay Gupta ?Did you meet Dr. Sanjay Gupta ?TIBET-SEEKERhttps://www.blogger.com/profile/03379410917028501628noreply@blogger.comtag:blogger.com,1999:blog-8155036766532593680.post-12738208632835549582016-04-09T08:52:40.797-07:002016-04-09T08:52:40.797-07:00 Got chill when reading this I love your outlook. Got chill when reading this I love your outlook.sdrdhttps://www.blogger.com/profile/01988746005995660372noreply@blogger.comtag:blogger.com,1999:blog-8155036766532593680.post-18220262592294332612016-01-23T05:24:22.740-08:002016-01-23T05:24:22.740-08:00The trembling guy, is that how a potentialist feel...The trembling guy, is that how a potentialist feel when he/she is lead to the real of the first limit ordinal? That is a cool thing :DAlejoM - The Bloodbenderhttps://www.blogger.com/profile/11488213819158085252noreply@blogger.com