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From: Eckard Blumschein on 14 Apr 2005 13:00 Well, I should avoid such a slip of my pen. But do you really not have more serious arguments? >> The set of real numbers between 0 and 1 is finite. > > Cool.
From: Giuseppe Bilotta on 14 Apr 2005 12:52 On Thu, 14 Apr 2005 19:00:49 +0200, Eckard Blumschein wrote: > serious It's very hard to keep serious reading your posts. But please don't let this bother you. Keep going. -- Giuseppe "Oblomov" Bilotta Hic manebimus optime
From: David C. Ullrich on 15 Apr 2005 06:39 On Thu, 14 Apr 2005 18:36:36 +0200, Eckard Blumschein <blumschein(a)et.uni-magdeburg.de> wrote: >On 4/14/2005 1:45 PM, David C. Ullrich wrote: >> On 13 Apr 2005 08:53:43 -0700, worldsofsolution(a)yahoo.com wrote: >> >>>There is something I've been wondering about cantor's proof: the >>>decimal number generated to prove the contradiction, was taken to be a >>>real number. There is a tacit assumption that all decimal numbers >>>represent a real number. Does that not require a proof? >> >> Yes. >> >> It's not hard to prove - exactly _how_ you prove it depends >> on exactly how you defined "real number". >> > >Because the discussion mostly deals with Cantor, Really? I thought that the discussion was about sets and real numbers. >I would like to suggest >preferring his definition. Hmm. I was not aware that Cantor _gave_ a definition of "real number". You'd know better than I would, of course. So tell me, what _was_ Cantor's definition of "real number"? ************************ David C. Ullrich
From: Alois Steindl on 15 Apr 2005 06:38 David C. Ullrich <ullrich(a)math.okstate.edu> writes: > Hmm. I was not aware that Cantor _gave_ a definition of > "real number". You'd know better than I would, of course. > So tell me, what _was_ Cantor's definition of "real number"? > > Hello, Aren't you aware that you shouldn't ask Eckart mathematical questions? Either he is too busy or too old to answer. Quite likely he will answer that he is only an engineer and need not deal with definitions. Nevertheless he is sure that he is right and understands more mathematics than anybody else (maybe Mýckenheim could be an exception). But maybe he comes up with a definition; I would of course be very astonished. SCNR Alois
From: Shmuel (Seymour J.) Metz on 14 Apr 2005 21:06
In <1113407623.729125.127220(a)l41g2000cwc.googlegroups.com>, on 04/13/2005 at 08:53 AM, worldsofsolution(a)yahoo.com said: >There is something I've been wondering about cantor's proof: the >decimal number generated to prove the contradiction, was taken to be >a real number. There is a tacit assumption that all decimal numbers >represent a real number. Does that not require a proof? Yes, and it's straightforward. Most expositions of proofs omit obvious steps. Of course, for new results you need to ensure that it really is obvious. -- Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel> Unsolicited bulk E-mail subject to legal action. I reserve the right to publicly post or ridicule any abusive E-mail. Reply to domain Patriot dot net user shmuel+news to contact me. Do not reply to spamtrap(a)library.lspace.org |