Date: Feb 14, 2013 6:44 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots
On Feb 14, 8:26 am, WM <mueck...@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

>

So we note that it makes perfect sense to ask

if potentially infinite sequences x and y are equal,

we have cases where they are not equal and cases

where they are equal. We also note that no

concept of completed is needed, so equality can

be demonstrated by induction.

So WMs statements are

there is a line l such that d and l

are equal as potentially infinite sequences.

there is no line l such that d and l

are equal as potentially infinite

sequences.

> 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