Article View: sci.logic
Article #818Re: A Guide for Cantor Cranks
From: Albrecht
Date: Thu, 24 Mar 2011 14:30
Date: Thu, 24 Mar 2011 14:30
39 lines
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3788 bytes
On 24 Mrz., 15:08, James Burns <burns...@osu.edu> wrote: > Albrecht wrote: > > On 24 Mrz., 10:31, William Hughes > > <wpihug...@gmail.com> wrote: > >>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? But you insist that the "behaviour" of > > a number like 3.1415... should be like the "behaviour" of > > a number like 0.75? > > > The axioms behind this view are silly. > > If I am not mistaken, there is only one axiom that > distinguishes infinite decimal numbers (real numbers) > from finite decimal numbers (rational numbers, or close > enough for our purposes). > > < For every non-empty set of real numbers, if it has > < an upper bound, then it has a least upper bound. > > Upper bound and least upper bound are defined in the > expected ways: > > Upper bound of set A == a real number greater than or > equal to every element of A > > Least upper bound of set A == an upper bound of A > less than or equal to every upper bound of A > > I just wanted to be sure: > do you find this axiom silly? Axiom?
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X-Google-Thread: 10cc56,bdbafb069b8118a7 X-Google-NewGroupId: yes X-Google-Thread: 109d8a,bdbafb069b8118a7 X-Google-NewGroupId: yes 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: gide4b186767d,gid9ef9b79ae9,gided4ff1f581,gid54ac8f410d,giddb42311052,domainid0,public,usenet X-Google-Language: ENGLISH,ASCII Path: arc1-ca.pugleaf.net!g2news2.google.com!postnews.google.com!w7g2000yqe.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 07:30:13 -0700 (PDT) Organization: http://groups.google.com Lines: 39 Message-ID: <be4cc683-a233-4ddc-b0b7-977464537c90@w7g2000yqe.googlegroups.com> References: <40e69d0c-eb77-4308-996e-c7dfc1a0ec1e@j13g2000pro.googlegroups.com> <2298d465-e708-4801-be12-12c714cd98dc@f36g2000pri.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> <4D8B5041.9060702@osu.edu> 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 1300977013 2394 127.0.0.1 (24 Mar 2011 14:30:13 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Thu, 24 Mar 2011 14:30:13 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: w7g2000yqe.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)