```Date: Jan 27, 2013 1:21 PM
Author: Jesse F. Hughes
Subject: Re: ZFC and God

WM <mueckenh@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.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 fas 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 terminatingdecimal representation.>> > 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 have> it just at hand, here it is again:> 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 is written as> 0.777...>> This is the definition that I agreed to.Er, no.  The definition that you agreed to is reproduced above.  You have toshow that the definition above is actually satisfied, i.e., that thereis a natural number k and a function f satisfying the appropriateconditions.You've done no such thing.Frankly, I'm a bit stunned that you're arguing that 7/9 has aterminating decimal representation, but as long as you're claiming so,then you need to stick to the definition we've agreed on.-- "Being who I am, I know that's a solution that will run in polynomialtime, but for the rest of you, it will take a while to figure that outand know why [...But] it's the same principle that makes n! such arapidly growing number."  James S. Harris solves Traveling Salesman
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