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,

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

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> > 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

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> 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.