Virgil
Posts:
4,491
Registered:
1/6/11
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Re: ZFC and God
Posted:
Jan 27, 2013 3:35 PM
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In article
<4258abaf-6627-4b00-8995-d4505279dab0@v5g2000yqg.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 27 Jan., 13:10, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> > WM <mueck...@rz.fh-augsburg.de> writes:
> > > On 26 Jan., 23:19, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> >
> > >> > It is unclear why you apparently are unable to understand, that we are
> > >> > working in the set of terminating decimals. Therefore the diagonal
> > >> > cannot be actually infinite, although there is no last digit.
> >
> > >> Let me ask you a very simple question.
> >
> > >> Is 0.777.... a terminating decimal representation or a
> > >> non-terminating decimal representation?
> >
> > > That depends on the domain where you work in. We have started to work
> > > in the domain of terminating decimals. Since the diagonal consists
> > > only of (changed) digits of these decimals, it is obviously a
> > > terminating decimal.
> > > Now, to answer your question: You did not say where you take 0.777...
> > > from. And obviously that cannot be determined from the digits, as I
> > > jusr explained.
> >
> > When I write 0.777..., I mean the number
> >
> > sum_i=1^oo 7 * 10^-i
> >
> > That is, for each i in N, the i'th digit of 0.777... is defined and is
> > 7.
>
>
> And do you have problems to find this confirmed as possible in the
> complete set of terminating decimals? Any digit or index missing?
The original problem was the countability of the set of real numbers
between 0 and 1, which cannot be represented by WM's terminating
decimals, or by terminating binaries, for that matter, but can be
represented by non-termnating decimals or nonterminating binaries.
> >
> > Do you agree that there is only one number satisfying that
> > description? Or are there two numbers that satisfy that description
> > and one of the numbers is terminating and the other non-terminating?
>
> I agree that this is a finite definition. But I said that we are
> working in the set of terminating decimals and identify numbers by
> their digits, indices or nodes. Is that hard to understand?
That you're saying it is not hard to understand,but that your saying it
has the power to make others conform is imossible to understand.
You are not here the all powerful professor in front of your captive
classes, and have no power to command.
> >
> > Let's suppose there *are* two different numbers, corresponding to the
> > terminating 0.777... and the non-terminating 0.777... . Then
> >
> > term. 0.777... = sum_i=1^oo 7*10^-i
> >
> > and also
> >
> > non-term. 0.777... = sum_i=1^oo 7*10^-i,
> >
> > but then, of course, term. 0.777... = non-term. 0.777... ! Oops!
> >
> > Moreover, neither term. 0.777... nor non-term 0.777... satisfy the
> > definition of terminating decimal that you previously agreed to,
> > namely
> >
> > 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.
> >
> > The "terminating" 0.777... has no finite length.
>
> Please let me know when you will have succeded in finding a 7 that is
> not in the set of all terminating decimals.
Please let us know why you think you have the power to make us play by
your silly rules?
That you want to restrict things to only finite sequences when others do
not choose to does not give you the power to do so.
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