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Article #72Re: A definition of an infinity, perhaps!?
From: Graham Cooper
Date: Thu, 13 Oct 2011 22:17
Date: Thu, 13 Oct 2011 22:17
75 lines
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4093 bytes
On Oct 14, 7:13 am, William Hughes <wpihug...@gmail.com> wrote: > On Oct 13, 12:39 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > > On 13 Okt., 15:29, William Hughes <wpihug...@gmail.com> wrote: > > > > So we are agreed that you can have a finished infinity > > > of symbols that contains a symbol for every natural number but does > > > not contain the symbol oo. (note that this finished infinity > > > does not have a largest element). > > > Of course, if there are no other arguments contradicting it. > > > > The first column contains every natural number > > > but does not contain oo, and the diagonal contains every natural > > > number but does not contain oo, They are identical. > > > And here is the argument contradicting it: > > The third side must also contain every natural number, but does not. > > There is no third side. > > A third side would have to be the last line. > > The fact that a limit, L, of things from the triangle > exists does not mean that L is part of the triangle. > > - William Hughes This is my spin on the "Infinite Triangle" using an INFINITE UNION OF SAMPLES Consider the sequence +------->... X ! <1> ! <12> ! <123> ! <1234> v ... Y The length is oo, but the width is finite So even if you DEFINE A LIMIT FOR Y->oo and no limit for X->oo The fact X=Y still implies (to WM atleast) that the FINISHED INFINITY still never exists. There is one more step required, for X & Y to reach infinity the sequences must be formatted as finite samples (prefixes) of infinite sequences and you consider the SAMPLES like so... +------->... ! <1...> ! <12...> ! <123...> ! <1234...> v ... Now the UNION of the above INFINITE SET = N since each sequence includes the previous sequence an infinite Union is possible and both LIMITS x->oo and y->oo are defined. Exists(i): i = oo Herc
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X-Google-Thread: db42311052,79e4b6580f667c81,start X-Google-Attributes: giddb42311052,public,usenet X-Google-NewGroupId: yes X-Google-Language: ENGLISH,ASCII Path: arc1-ca.pugleaf.net!g2news1.google.com!postnews.google.com!o19g2000vbk.googlegroups.com!not-for-mail From: Graham Cooper <grahamcooper7@gmail.com> Newsgroups: sci.physics.relativity,sci.physics,sci.math,rec.org.mensa,aus.science Subject: Re: A definition of an infinity, perhaps!? Date: Thu, 13 Oct 2011 15:17:23 -0700 (PDT) Organization: http://groups.google.com Lines: 75 Message-ID: <fbee0832-94fb-4643-8863-0e6e38c24cba@o19g2000vbk.googlegroups.com> References: <106ae260-7347-4e32-8771-3858a1503af9@g33g2000yqc.googlegroups.com> <ae3bf2b1-9a7d-4a05-863d-16a2227d249d@i16g2000vbk.googlegroups.com> <407d23dc-0b2a-4e85-9f32-24ecb0f0da66@u4g2000prl.googlegroups.com> <b8588c74-4a8b-46cc-bd00-ba6aaea44024@t4g2000vby.googlegroups.com> <1db4ffc4-5833-49d0-aaff-634a62ebe798@t4g2000vby.googlegroups.com> <e48d23fd-e404-43d4-86b5-898564dd3e02@dk6g2000vbb.googlegroups.com> <2178a7f7-398a-461f-96aa-f0d6c224e714@r1g2000yqm.googlegroups.com> <836f8708-f082-4aff-9e29-0e3f663dfff7@a25g2000yqi.googlegroups.com> <0e93c97c-c9ca-425a-b662-90e69a15b9b7@x7g2000yqn.googlegroups.com> <d8483257-60c6-448c-bbda-de3be7968edb@w23g2000vbx.googlegroups.com> <452a4dbd-24dc-4630-9bdd-b6a1f508c801@x7g2000yqn.googlegroups.com> <9f272b62-c5db-4a70-ae63-2de76ed93d17@q30g2000vbx.googlegroups.com> NNTP-Posting-Host: 114.72.222.67 Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable X-Trace: posting.google.com 1318544717 21330 127.0.0.1 (13 Oct 2011 22:25:17 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Thu, 13 Oct 2011 22:25:17 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: o19g2000vbk.googlegroups.com; posting-host=114.72.222.67; posting-account=EsDGawkAAAAN6xcF2fi-X0yb3ECD-3_I User-Agent: G2/1.0 X-Google-Web-Client: true X-Google-Header-Order: HNKUARELSC X-HTTP-UserAgent: Mozilla/5.0 (Windows NT 6.1) AppleWebKit/535.1 (KHTML, like Gecko) Chrome/14.0.835.202 Safari/535.1,gzip(gfe)