Date: Feb 13, 2013 2:54 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots
On 12 Feb., 20:40, William Hughes <wpihug...@gmail.com> wrote:

> > What do you understand by being equal "as potentially infinite

> > sequences"?

>

> two potentially infinite sequences x and y are

> equal iff every FIS of x is a FIS of y and

> every FIS of y is a FIS of x.

Every means: up to every natural number.

>

> You can use induction to show that two potentially

> infinite sequences are equal (you only need

> "every" not "all").

Up to every n there is a line l identical to d.

But according to your implicitely made assumption it should be true

for all n. The lines of the list, if written into one single line, L,

yield: The potentially infinite sequences L and d are equal.

123... = L

1

12

123

...

>

> Your first claim is that there is a line l such that

> d and l are equal as potentially infinite sequences.

For every n this is true.

>

> Your other claim is that there is no line

> l such that d and l are equal as potentially infinite

> sequences.

For every FIS of d there is a line. You cannot find a line for all FIS

(because all FIS do not exist).

>

> You are asserting a contradiction.

It is a contradiction only when confusing every and all.

Regards, WM