Date: Feb 13, 2013 2:54 AM
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
> 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
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.