Article View: sci.logic
Article #824Re: A Guide for Cantor Cranks
From: Albrecht
Date: Fri, 25 Mar 2011 00:05
Date: Fri, 25 Mar 2011 00:05
45 lines
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3856 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? No. I have the axiom of infinity in mind. And the combination of the power set axiom with the axiom of infinity. Without these axioms the interpretation of the diagonal argument of Cantor is completely different from the common interpretation. Best Albrecht
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X-Google-Thread: 10b271,bdbafb069b8118a7 X-Google-NewGroupId: yes X-Google-Thread: fd648,af7892021029fe4a X-Google-NewGroupId: yes X-Google-Attributes: gid54ac8f410d,giddb42311052,domainid0,public,usenet X-Google-Language: ENGLISH,ASCII Path: arc1-ca.pugleaf.net!g2news2.google.com!postnews.google.com!k7g2000yqj.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 17:05:33 -0700 (PDT) Organization: http://groups.google.com Lines: 45 Message-ID: <936fb9f1-da8e-4533-93a1-15cf5d060cc5@k7g2000yqj.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: 87.178.50.132 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: posting.google.com 1301011615 31606 127.0.0.1 (25 Mar 2011 00:06:55 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 25 Mar 2011 00:06:55 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: k7g2000yqj.googlegroups.com; posting-host=87.178.50.132; posting-account=6xUtvgkAAAD_jypmLa2oo2HnrV0e8X9q User-Agent: G2/1.0 X-HTTP-UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.1; de; rv:1.9.2.3) Gecko/20100401 Firefox/3.6.3 GTB7.1 (.NET CLR 3.5.30729),gzip(gfe)