Date: Feb 13, 2013 3:48 AM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article 
WM <> wrote:

> On 12 Feb., 20:40, William Hughes <> 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.

Which includes being up to all natural numbers.
> >
> > 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.

Only in Wolkenmuekenheim.

Since for every line of length n, d is of length at least n+1, at least
everywhere else besides Wolkenmuekenheim, WMs claim does not hold true
outside it.

And inside Wolkenmuekenheim all lines are finite.

> For every FIS of d there is a line. You cannot find a line for all FIS
> (because all FIS do not exist).

But for each finite line l,there is FIS of d longer than l.
> >
> > You are asserting a contradiction.

> It is a contradiction only when confusing every and all.

The only way that some statement about a natural can fail to be true for
all naturals is when there exists some natural for which it is false.