Date: Mar 1, 2013 5:51 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Mar 1, 10:33 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 1 Mrz., 15:50, William Hughes <wpihug...@gmail.com> wrote:
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> > On Mar 1, 2:47 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > On 1 Mrz., 13:14, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Mar 1, 12:19 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > On 28 Feb., 23:40, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > On Feb 28, 11:29 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > > > I think that there is a variable maximum or limit that depends (among
> > > > > > > others) on t.

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> > > > > > So what did the statement
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> > > > > >     There is no m(t).
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> > > > > > mean?
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> > > > > We cannot fix it in the sense required for "there is" of current
> > > > > mathematics.

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> > > > So at a given time t,
> > > > m has a value which is a
> > > > natural number, but we cannot
> > > > assign this natural number
> > > > to a function.

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> > > Can you find a largest natural number in your personal environment?
> > > Can you determine the largest natural number that your computer is
> > > able to compute?

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> > Well, I don't know the values, but I certainly can assume
> > they exist and do not change if time does not change.  So I can
> > have a(t), the largest number in my personal environment
> > at time t, and b(t) the largest number that my computer
> > is able to calculate at time t.  (I don't suppose that
> > the largest number that a given computer is able to
> > compute can change,

>
> That depends on the abbreviations the user invents (Ackermann, Knuth).
>

> > but certainly the computer
> > referred to as "my computer" can change).
> > I only need assume that the value of m exits and
> > does not change if time does not change and then
> > I can assign the value of m to a function of time

>
> The argument is not only time.


m can change even though the time does not ?


> But in general your description is
> acceptable.
>
> So what is your true opinion about this potential infinity which,
> contrary to finished infinity, is not self-contradictory and allows
> for all calculations required in analysis?


I
"Potential infinity" does not differ in any
essential way from "finished infinity".
The language changes a bit, and at times you need more words
but the behaviour is the same.

E.g

With finished infinity you do not have a largest
natural

With potential infinity you do not have a largest
non-variable natural

With finished infinity there is no line of L
that contains every FIS of d.

With potential infinity there is no line of L
that has a non-variable index and contains
every FIS of d

With finished infinity there are no balls
in the vase.

With potential infinity there are no balls
with a non-variable label in the vase.