Date: Jan 24, 2013 4:22 PM
Author: Virgil
Subject: Re: ZFC and God
In article

<50d48405-e046-47fe-93d0-70774eabb665@m12g2000yqp.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Jan., 13:56, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:

> > "Jesse F. Hughes" <je...@phiwumbda.org> writes:

> >

> > > Yes, but let's be perfectly clear here. What we have now is this:

> >

> > > a function t: N -> R such that, for all i in N, t(i) is a real

> > > number with terminating decimal representation. We'll write this as

> > > t_i and we'll write t_i(j) for the j'th digit of t_i (in its

> > > terminating representation, which is, of course, unique).

> >

> > > Let d in R be defined by

> >

> > > d(j) = 7 if t_j(j) != 7

> > > d(j) = 6 if t_j(j) = 6.

> >

> > ^ Should be 7, of course.

> >

> >

> >

> > > Clearly, for all j, d(j) != t_j(j) and hence d != t_j for any j in

> > > N.

> >

> > > Is this what you mean up 'til now?

> >

> > So, for instance, take the obvious enumeration of finite decimal

> > representations (in [0,1), of course)

> >

> > 0.0

> > 0.1

> > 0.2

> > 0.3

> > 0.4

> > 0.5

> > 0.6

> > 0.7

> > 0.8

> > 0.9

> > 0.11

> > 0.12

> > ...

> >

> > Clearly, t_i(i) = 0 for every i, and hence d_i = 7 for every i. Thus,

> > d = 0.777..., which is a number without any finite decimal

> > representation.

>

> As long as the line has a finite enumeration, also the column has.

Nonsense. As usual from WM.

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