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

<1b2bb717-425f-488d-b50c-e442f20af58d@fe28g2000vbb.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> 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.

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.

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