Date: Feb 26, 2013 4:54 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Feb 26, 6:11 pm, WM <> wrote:
> On 26 Feb., 13:11, William Hughes <> wrote:> On Feb 26, 12:47 pm, WM <> wrote:

> > We both agree
> >  There does not exist an m
> >  such that the mth line
> >  of L is coFIS with the diagonal
> >  (here we interpret "There does
> >  not exist" to mean "we cannot find").

> > So we agree any such m must be an
> > unfindable natural number.

> It is a variable that can take any natural number.

OK, so we have constant natural numbers
and variable natural numbers.

We agree that any such m cannot be
a constant natural number but must
be a variable natural number.

Now, in standard terminology (where there
is no such thing as a variable
natural number) we have
a natural number valued function of time
(or of the number of FISs of d that "actually
exist", an increasing function of time)
m(t). It is trivial to see that there
is an m(t) such that the "actually existing"
line with index m(t), contains all
"actually existing" FISs of d.
However, calling m(t) "the index of the line
that contains every FIS of d"
strains language beyond the breaking point.

Similarly, it follows by definition
of "actually existing", that
there is a time varying function max(t),
such that at any time max(t) is the maximum
of the "actually existing" natural numbers.
However, calling the function max(t)
the largest element of the potentially
infinite set |N, is silly.

Now no one can stop you using whatever
terminology you want. However, do not
expect that you can use idiotic terminology
without being considered an idiot.