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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