```Date: Feb 14, 2013 4:23 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <dc0f1cc8-0ece-48ee-97ca-c395fb109ffa@n6g2000vbf.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 13 Feb., 23:22, William Hughes <wpihug...@gmail.com> wrote:> > On Feb 13, 9:03 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> > <snip>> >> > > You cannot discern that two potentially infinity sequences are equal.> > > When will you understand that such a result requires completeness?> >> > Nope> >> > Two potentially infinite sequences x and y are> > equal iff for every natural number n, the> > nth FIS of x is equal to the nth FIS of y> > And just this criterion is satisfied for the system> > 1> 12> 123> ...> > For every n all FISs of d are identical with all FISs of line n.But that is not at all the same thing.Note that even the actually infinite set of FISs of what you call a merely potentially finite sequence does not contain that sequence as a member.What WM is claiming that given the infinite sequence of finite sequences    l1=1, l2 = 12, l3 = 123,  ...and the infinite sequence d = 1,2,3,...that l1 and l1,l2, and l1, l2, l3  and so on are FISs of d.But, at least  outside of Wolkenmuekenheim, it is not so.> > And the three points stand for every finite number, but not for all.If not for all, some must be missing, so which are missing?> >> > Consider the list of potentially infinite sequence> > L1=> > 1000...> > 11000...> > 111000...> > ...> >> > L2=> > 111...> > 11000...> > 111000...> > ...> >> > The diagonals are both> > d=111...> > And again you confuse every with all.Can WM distinguish between not every and not all?> >> > It makes perfect sense to say that there> > is no line in L1 that is equal> > to d> > Perfect sense?Far more perfect than WM every makes.> Do you claim that the list> 1> 12> 123> ...> does not contain every FIS of d?For the d above, namely d = 111...,  your list certainly does not any FIS of that d of more  than one digit in length.> Do you claim that there are two or more FISs of d that require more> than one line for their accomodation?All of them  cannot be accomodated at all> > We can use induction to show that!> > Ponder about this question and then try to make perfect sense. Perfect sense and WM are incompossible.--
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