Date: Feb 14, 2013 2:26 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots
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.

> No concept of completeness is needed or used.

That means we have to go to n only.

>

> E.G,

>

> we can use induction to show

>

> x={1,1+2,1+2+3,...,1+2+...+n,...}

>

> is equal to

>

> y={(1)(2)/2,(2)(3)/2,(3)(4)/2,...,n(n+1)/2,...}

And the three points stand for every finite number, but not for all.

>

> 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.

>

> It makes perfect sense to say that there

> is no line in L1 that is equal

> to d

Perfect sense?

Do you claim that the list

1

12

123

...

does not contain every FIS of d?

Do you claim that there are two or more FISs of d that require more

than one line for their accomodation?

We can use induction to show that!

Ponder about this question and then try to make perfect sense.

Regards, WM