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Topic: Matheology � 258
Replies: 53   Last Post: May 11, 2013 10:07 PM

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 gus gassmann Posts: 60 Registered: 7/26/12
Re: Matheology § 258
Posted: May 7, 2013 10:16 PM

On 07/05/2013 5:56 PM, Virgil wrote:
> In article <kmbo3d\$e9h\$1@Kil-nws-1.UCIS.Dal.Ca>,
> Gus Gassmann <noone@nospam.com> wrote:

>> It is really too bad that the great Professor is simply too dense to
>> understand and use the following:
>>
>> A finite set of natural numbers contains a largest element.
>> An infinite set of natural numbers does not contain a largest element.

>
> Even more generally, a finite ordered set with no largest member is
> empty, but a non-empty ordered set with no largest member cannot be
> finite.

Sure. But one step at a time.

A finite set {n_1, n_2, ... n_k} of natural numbers contains a largest
element. Hence

U {i=1,...,k} FISON(n_i) = FISON(m) where m = max{n_1, n_2, ..., n_k}

But this identity breaks down when the index set does not have a maximal
element. I said "understand *and use*". Of course it is clear that the
good Professor cannot do either.