🚀 go-pugleaf

In article <332FC191.167EB0E7@clipper.ens.fr>, David Madore
<madore@clipper.ens.fr> writes
>Jaime Pina wrote:
>Jaime Pina wrote:
>>         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.
>
>Here is a proof that all real numbers are interesting:
>Let I be the set of interesting real numbers.
>  * I is not empty because 0, 1, e and pi are certainly in I.
>  * Any number sufficiently close to a given interesting number is
>interesting.
>(For example, a number which has the same first billion decimals as pi
>is clearly interesting.)
The set of numbers with the same first billion decimals as pi is
uncountably infinite, with the same cardinal number as the reals - this
is therefore a rather large claim.  I would find it hard to work up much
interest in more than one or two of them!
>Therefore I is open.
>  * A number which is the limit of a convergent sequence of interesting
>numbers
>is certainly interesting. Therefore I is closed.
>
>But R is connected. Therefore I=R, and all real numbers are interesting.
>QED.
>
>     David A. Madore
>    (david.madore@ens.fr,
>     http://www.eleves.ens.fr:8080/home/madore/index.html.en)

-- 

Martin Ward

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"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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