Article View: sci.logic
Article #816Re: A Guide for Cantor Cranks
From: Albrecht
Date: Thu, 24 Mar 2011 12:30
Date: Thu, 24 Mar 2011 12:30
69 lines
4388 bytes
4388 bytes
On 24 Mrz., 12:18, William Hughes <wpihug...@gmail.com> wrote: > On Mar 24, 7:12 am, Albrecht <albst...@gmx.de> wrote: > > > > > > > > > > > On 24 Mrz., 10:31, William Hughes <wpihug...@gmail.com> wrote: > > > > Recall > > > The anti-diagonal is formed by taking the > > > diagonal and changing every 0 to 1 and 1 to 0. > > > Any claim that the anti-diagonal does not exist is > > > silly. Any claim that the anti-diagonal is equal to > > > a row of the list is silly. > > > On Mar 24, 4:51 am, Albrecht <albst...@gmx.de> wrote: > > > > <snip> > > > > > Any claim that an irrational decimal number exists is silly. > > > > > Pi has to be the limit of the serie > > > > > 3/1, 31/10, 314/100, 3141/1000, 31415/10000, ... > > > > > If you claim the existence of an irrational decimal number you claim > > > > the existence of the number > > > > > 31415.../10000... > > > > > with infinite numerator and inifite denominator. > > > > Absolute piffle. There is no reason that defining the > > > existence of the limit of finite ratios means that you > > > have to define either infinite quantities, or the ratio > > > of infinite quantities. > > > So you admit that an infinite decimal number has crucial other > > properties than a finite decimal number? > >You admit that a number like > > 3.1415... is crucial different from a number like 0.75? > > Nope. I said nothing about the differences between > an irrational number and a rational number. > > > But you insist that the "behaviour" of a number like 3.1415... should > > be like the "behaviour" of a number like 0.75? > > I said nothing of the sort. > > My point is that while you need infinite sequences > of *finite* rations to > definite irrational numbers, you don't need either > infinite quantities or the ratio of infinite quantities. > You define the number 3.1415... as the limit of the infinite sequence. And you claim that these sort of "decimal numbers" could be handled like decimal numbers which are defined as ratios. That's only wishful thinking. And the best proof that this view is nonsensical is Cantor's well known diagonal argument. Best Albrecht
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X-Google-Thread: f8362,bdbafb069b8118a7 X-Google-NewGroupId: yes X-Google-Thread: 10b271,bdbafb069b8118a7 X-Google-NewGroupId: yes X-Google-Thread: fd648,af7892021029fe4a X-Google-NewGroupId: yes X-Google-Attributes: gided4ff1f581,gid54ac8f410d,giddb42311052,domainid0,public,usenet X-Google-Language: ENGLISH,ASCII Path: arc1-ca.pugleaf.net!g2news2.google.com!postnews.google.com!k9g2000yqi.googlegroups.com!not-for-mail From: Albrecht <albstorz@gmx.de> Newsgroups: sci.logic,sci.math,comp.theory,sci.physics,aus.science Subject: Re: A Guide for Cantor Cranks Date: Thu, 24 Mar 2011 05:30:11 -0700 (PDT) Organization: http://groups.google.com Lines: 69 Message-ID: <86b56236-ef58-4d99-a0c4-5bc21342062e@k9g2000yqi.googlegroups.com> References: <40e69d0c-eb77-4308-996e-c7dfc1a0ec1e@j13g2000pro.googlegroups.com> <2e445897-6fc0-488d-9ab5-fcd1c7dc703d@f30g2000yqa.googlegroups.com> <efc21f2f-acb7-475d-87ab-fbfa35208c4c@o15g2000prn.googlegroups.com> <9c851574-eb70-45c4-b6e3-9351a7679223@k30g2000yqb.googlegroups.com> <92a4e0aa-6497-4357-8a6b-ecc706fa10f5@d26g2000prn.googlegroups.com> <5d2c87a8-5926-4b27-a445-3bc3ab5c98d0@u3g2000vbe.googlegroups.com> <35760f05-df0e-4c29-85c0-08f98cf10a42@s18g2000prg.googlegroups.com> <521e5cfe-5269-4d9a-ab45-5e8cf597b2d1@y31g2000vbp.googlegroups.com> <971970b6-b722-4f38-96cb-4aef5f17e96e@b22g2000prb.googlegroups.com> <d9d86644-ea52-4f53-ba2f-42d2718630c0@k7g2000yqj.googlegroups.com> <b05355b2-d80e-47ec-9c3b-43e7bc40ab32@22g2000prx.googlegroups.com> <f7d9f169-c407-4b78-9190-486abbad7a04@i39g2000prd.googlegroups.com> NNTP-Posting-Host: 78.42.127.29 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: posting.google.com 1300969811 32523 127.0.0.1 (24 Mar 2011 12:30:11 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Thu, 24 Mar 2011 12:30:11 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: k9g2000yqi.googlegroups.com; posting-host=78.42.127.29; posting-account=6xUtvgkAAAD_jypmLa2oo2HnrV0e8X9q User-Agent: G2/1.0 X-HTTP-UserAgent: Mozilla/5.0 (Windows NT 5.1; rv:2.0) Gecko/20100101 Firefox/4.0,gzip(gfe)