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Article #124Re: Pi day
From: K. Edgcombe
Date: Wed, 19 Mar 1997 00:00
Date: Wed, 19 Mar 1997 00:00
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In article <Pine.GSO.3.95.970318235548.23662A-100000@shrike.depaul.edu>,
Jaime Pina <jpina@shrike.depaul.edu> wrote:
>On Tue, 18 Mar 1997, Ulrich Berger wrote:
>
>{>
>{>But any number in any range is interesting, don't you know that?
>{>For, if there were any uninteresting numbers, then there would be such a
>{>thing like the SMALLEST uninteresting number. Obviously this would make
>{>this number very interesting. This is a contradiction, and therefore
>{>there is no uninteresting number!
>
> WRONG! If there are uninteresting numbers, there does not have to
>be a SMALLEST uninteresting number, just like there is no smallest number
>in the real numbers.
I think the original discussion was about the natural numbers (the non-negative
integers), and it is clear that the poster of the above proof was thinking of
the natural numbers. By the well-ordering axiom, therefore, the proof holds.
By the way, even if you think someone is wrong, there is no need to SHOUT.
Katy Edgcombe
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X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f458d,30fff994c7ddd7d9 X-Google-Attributes: gidf458d,public X-Google-Thread: 109d8a,30fff994c7ddd7d9 X-Google-Attributes: gid109d8a,public X-Google-Thread: 1077c2,30fff994c7ddd7d9 X-Google-Attributes: gid1077c2,public X-Google-Thread: f7972,30fff994c7ddd7d9 X-Google-Attributes: gidf7972,public X-Google-Thread: 1130d6,30fff994c7ddd7d9 X-Google-Attributes: gid1130d6,public X-Google-Thread: 10d67e,30fff994c7ddd7d9 X-Google-Attributes: gid10d67e,public From: ke10@cus.cam.ac.uk (K. Edgcombe) Subject: Re: Pi day Date: 1997/03/19 Message-ID: <5gob11$6sf@lyra.csx.cam.ac.uk> X-Deja-AN: 226679598 References: <8WRuzAAXBILzEwKP@ward-hull.demon.co.uk> <332EB53C.584B@pap.univie.ac.at> <Pine.GSO.3.95.970318235548.23662A-100000@shrike.depaul.edu> Organization: University of Cambridge, England Newsgroups: uk.education.maths,alt.uu.math.misc,aus.mathematics,can.schoolnet.math.sr,alt.math.recreational,sci.math