Date: Feb 9, 2013 3:59 PM Author: Virgil Subject: Re: Matheology � 222 Back to the roots In article

<436a21e4-20db-40ee-a5b5-ffd291253d33@fw24g2000vbb.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 8 Feb., 23:52, Virgil <vir...@ligriv.com> wrote:

> > In article

> > <64c6e6d9-d039-48bf-9cd6-7c614cee3...@j4g2000vby.googlegroups.com>,

> >

> >

> >

> >

> >

> > WM <mueck...@rz.fh-augsburg.de> wrote:

> > > On 8 Feb., 23:26, William Hughes <wpihug...@gmail.com> wrote:

> > > > More WM logic

> >

> > > > L is a potentially infinite

> > > > list and d is the potentially infinite

> > > > anti-diagonal

> >

> > > > From

> > > > i. For every natural number n, d

> > > > is not the nth line of L

> >

> > > correct.

> >

> > > > ii. i. implies that there is no

> > > > natural number m such that

> > > > d is the mth line of L

> >

> > > No such m can be fixed.

> >

> > It is "fixed" in the sense of not existing at all!

> >

> >

> >

> > > > iii. d may or may not be a line of L

> >

> > > There is no part of d(potential) that is surpassing every line of a

> > > suitable list.

> >

> > If every member of the list has a last digit but d does not,

>

> That is one side of the medal, but it is not the only side.

>

> It is exactly as if you would prove that the even numnbers are larger

> than the odd numbers, by showing that for every off number there is a

> larger even number. Of course the latter is right, but it does not

> prove the claim.

It does prove that there is an even as large as any given odd, which is

more to the point.

>

> > then for

> > every member of the list there will be a first FIS of d surpassing it,

>

> and for every FIS of d there will be a first line of the remaining

> list surpassing it.

But no finite cap on the length of d unless there is finite cap on the

lengths of the set of FISs, which there is not.

And in standard set theories not finite means actually infinite.

>

> > and following it, a lot more of them following that first one..

>

> and following this first line there a lot more with the same surplus.

But no finite cap on either, thus an actual infinity of both.

> >

> > At least outside the idiotic constraints of WMytheology.

>

> There are no constraints. Is every FIS of d surpassed by a line of the

> list or is there a first FIS that is not surpassed? In mathematics the

> defender of such a position should be able to either prove it or to

> show an example.

But equally, every line of the list is surpassed by a FIS, thus both the

set of lines in the list AND the set of FISs of the diagonal must be

not-finite. Each is a strictly increasing in lengths sequence without a

maximum so is clearly NOT FINITE.

And NOT FINITE means INFINITE everywhere outside WMytheology.

>

> You have already agreed hat d is not actually infinite

When or where do you allege that I have done anything so foolish?

In ZF, and elsewhere outside Wolkenmuekenheim , there is provably a set

having a first element and for each element another greater than it.

In S+ZF, for example, each member of such a set is a proper subset of

each of its successors.

Such sets are provably not finite. Which everywhere outside of

Wolkenmuekenheim is also called infinite.

--