```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:>>>>>>>>>> > On Mar 1, 2:47 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > On 1 Mrz., 13:14, William Hughes <wpihug...@gmail.com> wrote:>> > > > On Mar 1, 12:19 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > > On 28 Feb., 23:40, William Hughes <wpihug...@gmail.com> wrote:>> > > > > > On Feb 28, 11:29 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > > > > > > I think that there is a variable maximum or limit that depends (among> > > > > > > others) on t.>> > > > > > So what did the statement>> > > > > >     There is no m(t).>> > > > > > mean?>> > > > > We cannot fix it in the sense required for "there is" of current> > > > > mathematics.>> > > > 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.>> > > 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?>> > 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 anyessential way from "finished infinity".The language changes a bit, and at times you need more wordsbut the behaviour is the same.E.gWith finished infinity you do not have a largestnaturalWith potential infinity you do not have a largestnon-variable naturalWith finished infinity there is no line of Lthat contains every FIS of d.With potential infinity there is no line of Lthat has a non-variable index and containsevery FIS of dWith finished infinity there are no ballsin the vase.With potential infinity there are no ballswith a non-variable label in the vase.
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