Article View: sci.logic
Article #845Re: A Guide for Cantor Cranks
From: Graham Cooper
Date: Mon, 21 Mar 2011 07:09
Date: Mon, 21 Mar 2011 07:09
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4333 bytes
On Mar 21, 4:54 pm, William Hughes <wpihug...@gmail.com> wrote: > On Mar 21, 3:33 am, Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > > > On Mar 21, 2:30 pm, William Hughes <wpihug...@gmail.com> wrote: > > > > > My point is you can't support your claim with 2 given diagonals. > > > > My claim is that given a list of binary sequences I can find a > > > sequence > > > not on the list. > > > > To support this claim I need only one diagonal. When you gave me > > > two diagonals I chose one and supported the claim. > > > > Your claim that you can get a generalized diagonal with any finite > > > prefix is true, but irrelevant. You cannot set the generalized > > > diagonal to an arbitrary sequence. > > > - William Hughes > > > You haven't proven your sequence is not on the list in the 2 diagonal > > version. > > > AD1 = 1110... > > AD2 = 0110... > > > Can you prove EITHER real is missing from my (secret) list given only > > the above? > > > IF YES, then by all means do so! > > There is a sequence not on your secret list that starts > 1100. Proof: the n'th digit means that sequence is not > the n'th line of the list. There may be other sequences that > starts 1110 on your secret list. > -William Hughes- Well that was concise! But it's invalid due to the pigeon hole principle. My similar claim to yours is: no matter what numbers I put into the pigeon holes, there are always more empty pigeon holes than filled pigeon holes. Here is my first attempt at the proof. -1--2--3--4--5--6--7--8--9--0- [ ][ ][ ][ ][ ][ ][ ][ ][ ][ ] I'm going to put a pigeon in pigeon hole number 7! -1--2--3--4--5--6--7--8--9--0- [ ][ ][ ][ ][ ][ ][P][ ][ ][ ] Full pigeon holes = 1 Empty pigeon holes = 9 So my claim that : no matter what numbers I put into the pigeon holes, there are always more empty pigeon holes than filled pigeon holes. HOLDS but is not PROVEN!
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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!d26g2000prn.googlegroups.com!not-for-mail From: Graham Cooper <grahamcooper7@gmail.com> Newsgroups: sci.logic,sci.math,comp.theory,sci.physics,aus.science Subject: Re: A Guide for Cantor Cranks Date: Mon, 21 Mar 2011 00:09:43 -0700 (PDT) Organization: http://groups.google.com Lines: 75 Message-ID: <92a4e0aa-6497-4357-8a6b-ecc706fa10f5@d26g2000prn.googlegroups.com> References: <40e69d0c-eb77-4308-996e-c7dfc1a0ec1e@j13g2000pro.googlegroups.com> <d3c279c6-b0d0-4da0-9360-d0c7a91980fb@n2g2000prj.googlegroups.com> <adc08cec-9301-4754-9fcf-61ffc38b5b74@s18g2000vbe.googlegroups.com> <ad7ef639-a0c7-4421-a8ca-1f121439228d@b4g2000vby.googlegroups.com> <9268ac3b-e542-412c-8927-a2fe082e6fb0@f31g2000pri.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> NNTP-Posting-Host: 120.17.70.168 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: posting.google.com 1300691383 15605 127.0.0.1 (21 Mar 2011 07:09:43 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Mon, 21 Mar 2011 07:09:43 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: d26g2000prn.googlegroups.com; posting-host=120.17.70.168; posting-account=EsDGawkAAAAN6xcF2fi-X0yb3ECD-3_I User-Agent: G2/1.0 X-HTTP-UserAgent: Mozilla/4.0 (compatible; MSIE 8.0; Windows NT 6.1; Trident/4.0; SLCC2; .NET CLR 2.0.50727; .NET CLR 3.5.30729; .NET CLR 3.0.30729; HPMTDF; BRI/2),gzip(gfe)