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Topic: Matheology § 259
Replies: 9   Last Post: May 2, 2013 4:46 PM

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Posts: 8,833
Registered: 1/6/11
Re: Matheology � 259
Posted: May 1, 2013 3:43 PM
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In article
WM <> wrote:

> Matheology § 259
> A discussion in sci.logic yielded the following remarkable results
> with respect to a list having infinitely many lines
> {1}
> {1} U {2}
> {1} U {2} U {3}
> ...
> Each line contains as many unioned sets as its line number indicates
> but does not contain a line |N, since each line has a finite last
> number n.
> On the other hand, there are infinitely many lines and, as each line
> adds one number, there are infinitely many numbers in the list. Since,
> by construction, every finite initial segment s_n = {1, 2, 3, ..., n}
> is in one single line, all finite initial segments are in one single
> line.

While each FISON fills in one single line, that does not put any two
FISONs on the same line, and certainly does not, at least outside
Wolkenmuekenheim, put all lines in any one line.

> But |N is not more than all its finite initial segments.

Yes it is, as it is not merely a list of all its FISONs but the union of
all of them, which is not the same thing, except possibly in the wilds
of Wolkenmuekenheim, .
> Otherwise there must exist at least two finite initial segments such
> that
> exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k.

Certainly not outside his Wolkenmuekenheim. While WM keeps claiming itt,
he has yet to proffer any evidence for it, much less any proof of it.

Thus if it is to hold at all, it can only hold where WM's word is law
and his claims do not need proofs: inside Wolkenmuekenheim,

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