```Date: Jan 27, 2013 1:33 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

On 27 Jan., 19:21, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:> WM <mueck...@rz.fh-augsburg.de> writes:> > On 27 Jan., 18:44, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:>> >> 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?>> Because, of course, you accepted the following definition:>>   Let x be a real number in [0,1].  We say that x has a terminating>   decimal representation iff there is a natural number k and a>   function f:{1,...,k} -> {0,...,9} such that>>    x = sum_i=1^k f(i) * 10^-i.I did not fix k but only assumed that it is a natural number.>> Thus, if you claim that 0.777... has a terminating representation,> then you must show that there is a natural number k and a function f> as above such that>>   0.777... = sum_i=1^k f(i) * 10^-i.>> Else, you have no cause to claim that 0.777... has a terminating> decimal representation.>You have no cause to claim the contrary, since there is no index(natural number) infinitely many counts away from the decimal point.>> > This is the definition that I agreed to.>> Frankly, I'm a bit stunned that you're arguing that 7/9 has a> terminating decimal representation, but as long as you're claiming so,> then you need to stick to the definition we've agreed on.I am not claiming that 7/9 ot 1/3 or sqrt(2) have decimalrepresentations at all.Just the contrary. But I am claiming that all decimal representationsthat exist in the domain of terminating decimals are terminating, inparticular the diagonal of a Cantor-list, as long as we work in thedomain of terminating decimal representations.If you insist in a non-terminating one, please show it!Regards, WM
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