🚀 go-pugleaf

In article <5gob11$6sf@lyra.csx.cam.ac.uk>, "K. Edgcombe"
<ke10@cus.cam.ac.uk> writes
>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

I was referring to real numbers (like pi - see the subject line) so
Jaime's crticism is valid.  I presume Ulrich was thinking of the natural
numbers, or possibly the rationals, or possibly rationals of the form
a/b where a,b are natural numbers with a<=31 and b<=12.  Any of these
sets can be well-ordered, and then Ulrich's argument "works" as Katy
says.

I like this argument, but of course it has a more subtle flaw...
-- 

Martin Ward

_________________________________________________________________________

"When *I* use a word", Humpty Dumpty said in rather a scornful tone, "it
 means just what I choose it to mean - neither more nor less".
"The question is", said Alice, "whether you *can* make words mean so many
 different things".
"The question is", said Humpty-Dumpty, "which is to be master - that's all".

"Through the Looking-Glass" - Lewis Carroll.
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