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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