Article View: sci.logic
Article #822Re: A Guide for Cantor Cranks
From: Virgil
Date: Thu, 24 Mar 2011 19:15
Date: Thu, 24 Mar 2011 19:15
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2911 bytes
In article <971970b6-b722-4f38-96cb-4aef5f17e96e@b22g2000prb.googlegroups.com>, Albrecht <albstorz@gmx.de> wrote: > Any claim that an irrational decimal number exists is silly. The issues of whether a real number exists and whether it has a terminating decimal representation are quite distinct. And the lack of such a decimal representation does not prevent a real number from existing. For one formulation of real numbers, any non-empty set of rationals that is bounded above determines a unique real number as its least upper bound. > > 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. There is a distinction between a numeral ands the number wwhich it represents. In particular, nothing in the construction of the set of real numbers requires a real number to have a decimal representation.
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<40e69d0c-eb77-4308-996e-c7dfc1a0ec1e@j13g2000pro.googlegroups.com> <07a61ecc-e3fd-4304-9977-f4f2724ef652@w21g2000yqm.googlegroups.com> <83c8a047-2cc6-4ed2-a74f-8329656c4f9f@j35g2000prb.googlegroups.com> <2d9a4e44-18dc-43fd-bec1-056b7b4ba26d@x11g2000yqc.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>Show Full Headers
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X-Google-Thread: db42311052,af7892021029fe4a X-Google-Attributes: giddb42311052,public,usenet X-Google-NewGroupId: yes X-Google-Language: ENGLISH,ASCII-7-bit Path: arc1-ca.pugleaf.net!g2news1.google.com!news2.google.com!border1.nntp.dca.giganews.com!nntp.giganews.com!news-out.readnews.com!transit3.readnews.com!s09-10.readnews.com!posts.news.usenetmonster.com!nnrp3-unl.asbnva.usenetmonster.com!not-for-mail From: Virgil <Vir@gil.Gil> Newsgroups: sci.logic,sci.math,comp.theory,sci.physics,aus.science Subject: Re: A Guide for Cantor Cranks Organization: Ligriv References: <40e69d0c-eb77-4308-996e-c7dfc1a0ec1e@j13g2000pro.googlegroups.com> <07a61ecc-e3fd-4304-9977-f4f2724ef652@w21g2000yqm.googlegroups.com> <83c8a047-2cc6-4ed2-a74f-8329656c4f9f@j35g2000prb.googlegroups.com> <2d9a4e44-18dc-43fd-bec1-056b7b4ba26d@x11g2000yqc.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> User-Agent: MT-NewsWatcher/3.5.2 (PPC Mac OS X) Date: Thu, 24 Mar 2011 13:15:48 -0600 Message-ID: <Vir-4E4B33.13154824032011@BIGNEWS.USENETMONSTER.COM> Lines: 30 NNTP-Posting-Host: 6c4aa36e.unlimited.usenetmonster.com X-Trace: DXC=bT9BMAiB7e\hM`8Gf:9eLZk\2KDSF=2@RFV0LA4MIjQ[mTIDj6@1Wa\0e<5N2]Xi1\IL[5j@Rb::Qk`d>b@`C=dTYIdo?66jkd\[99WKP@jcEQ X-Complaints-To: killthespammer@usenetmonster.com