```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 infiniteWhen 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.--
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