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 <mueck...@rz.fh-augsburg.de> wrote:

> On 26 Feb., 13:11, William Hughes <wpihug...@gmail.com> wrote:> On Feb 26, 12:47 pm, WM <mueck...@rz.fh-augsburg.de> 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.