Date: Feb 13, 2013 3:48 AM
Subject: Re: Matheology � 222 Back to the roots
WM <email@example.com> 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
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.