```Date: Jan 27, 2013 1:00 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

On 27 Jan., 18:44, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:>> > 0.7 is terminating.> > if 0.777...777 with n digits is terminating, then also 0.777...7777> > with n+1 digits is terminating. Therefore there is no upper limit for> > the number of digits in a terminating decimal. This fact is usually> > denoted by "infinite" and abbreviated by "...".>> Are you suggesting that 0.777... is *both* an infinite and terminating> expansion?In my opinion infinite has only one meaning, namely potenial infinity.The set N is potentially infinite. There is no upper thresholdalthough every FISON is finite. - And there is nothing else.By the AxInf we get a second infinity, namely a set N that has Aelements, where for every n in N: A > n.If someone believes that this axiom is better than the axiom thatthere are 10 different naturals with sum 10, then he should try tofind evidence. Hitherto I have not seen eveidence provided by you thatAxInf would be useful or required.> Anyway, you haven't proved that there is a function>>   f:{1,...,k} -> {0,...,9}>> as required by *your* definition of terminating decimal, so you have> not shown that 0.777... is a terminating decimal.You are wrong. Can't you understand? All natural numbers are finite.Why the heck should I define a single k?>> > Note, there is another meaning of infinite, namely "actually> > infinite". Those who adhere to that notion *in mathematics* should> > show that it differs from "potentially infinite" *in mathematics*,> > i.e., expressible by digits.>> Well, I don't understand why anyone would wish to show that.Perhaps in order to show that matheology is not complete nonsense?> But,> regardless, this is beside the point.  I'm asking for a proof that> 0.777... is terminating according to the definition of terminating> that you agreed to.I did this in my last posting. Please look it up there. Well as I haveit just at hand, here it is again:0.7 is terminating.if 0.777...777 with n digits is terminating, then also 0.777...7777with n+1 digits is terminating. Therefore there is no upper limit forthe number of digits in a terminating decimal. This is written as0.777...This is the definition that I agreed to.Regards, WM
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