Date: Mar 20, 2013 4:27 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<a692afc1-337d-47f2-9b7f-2e6f838ff3d0@r8g2000vbj.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 20 Mrz., 19:44, Virgil <vir...@ligriv.com> wrote:
>

> > > Either there is a list that contains everyting that the list contins
> > > in two or more lines.

> >
> > Since each line has a successor  line and is a proper subset of that
> > successor line, the only "escape" is to have a nonempty set of lines
> > with no last line.

>
> What should a missing last line help?


A nonempty set of lines with no last line shows, among other things,
that the empty set of lines will not work.

> As it is not present in the
> list, it cannot change the contents of the list.


On the contrary, a nonempty set of lines WITH a last line necessarily
omits all naturals not in that last line

but a nonempty set of lines WITHOUT a last line doesn't omit the
naturals of any line.

> But every line, that
> is not the last line and, therefore, is not missing, can be made
> missing without changing the contents of the list.


It is still both necessary and sufficient for a set of line/FISONs to
contain all naturals that that set b infinite, thus be both not empty
and not have either a last line or largest FISON.
>
> > > Since contents can only exist in lines, and since every line is
> > > superset to all its predecessors, the proof is correct. It shows that
> > > actual infinity is unreasonable.

> >
> > It does not show any such thing

>
> You could as well refrain from declaming assertions.




Why must we refrain from doing what WM is notorious for doing? Here is

> sci.logic, not spec.tacle.

Wm often makes spectatular claims then spectacularly fails to justify
them.

Like his claim to a linear map from the set of binary sequences through
the reals to the set of all paths in a Complete Infinite Binary Tree.
--