Date: Jan 28, 2013 9:57 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God
On 28 Jan., 12:44, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

> WM <mueck...@rz.fh-augsburg.de> writes:

> > On 27 Jan., 23:27, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

>

> >> >> it follows *FROM THE AGREED DEFINITION* that 0.777... has no

> >> >> terminating decimal representation.

>

> >> > Show that in your 0.777..., and in particular in the anti-diagonal of

> >> > a list of terminating decimals, there is an index k that does not

> >> > belong to a FISON {1, 2, ..., n}.

>

> >> Utterly irrelevant to the matter at hand. Evidently, you don't

> >> understand the definition you agreed to.

>

> > Please let me know where I agreed to that definition.

> > Of course, when working in the terminating decimals, every anti-

> > diagonal is terminating.

>

> In the post with

>

> Message-ID: <06a85bef-99c1-4104-862c-27351c153ccb@f6g2000yqm.googlegroups.com>

>

> we had the following exchange:

>

> ,----

> | > Let's state the definition explicitly then:

> | >

> | > 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.

> | >

> | > Right?

> |

> | Right.

But you forget that we had agreed that we are working in the set F of

all terminating decimals to construct a diagonal or 0.777... . Now

find out which of the digits of 0.777... that is constructed of

numbers of F has not a finite index k.

Regards, WM