```Date: Jan 25, 2013 3:47 AM
Author: Virgil
Subject: Re: ZFC and God

In article <e05afbc8-2ffc-4abb-bd67-0d8edf22f451@u7g2000yqg.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 25 Jan., 01:39, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:> > WM <mueck...@rz.fh-augsburg.de> writes:> > > On 24 Jan., 14:16, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:> > >> WM <mueck...@rz.fh-augsburg.de> writes:> > >> > You will have have recognized that here the diagonal argument is> > >> > applied. It is obvious that up to every line = column the list is a> > >> > square.> >> > >> It is clear that, for all j, d(j) != t_j(j) and hence d != t_j.  If> > >> that's what you mean by the diagonal argument, great!> >> > >> Once again, however, you say something that has no clear meaning to> > >> me.  Can you clarify "It is obvious that up to every line = column the> > >> list is a square?"  I've no clue what it means.> >> > > Then ponder a while about the following sequence> >> > > d> >> > > d1> > > 2d> >> > > d11> > > 2d2> > > 33d> >> > > and so on. In every square there are as many d's as lines. The same> > > could be shown for the columns.> >> > Yes, in this sequence of three squares, what you say is true.> > Is there a first square where my observation would fail?Since you claim every line is necessarily finite, but the number of lines is not, there will be a number of lines greater than the number of digits in your finite first line.When you have more lines than you have digits in your first line, and, you claim fails!> >> > But none of this is relevant, because we've explicitly defined the> > anti-diagonal d and it is a triviality to see that it is an infinite> > sequence of non-zero and non-nine digits.  And this fact really has> > nothing at all to do with limits of sequences of squares.  It is all> > perfectly explicit.> > Here you again intermingle potential and actual.No, YOU are the one trying to do that. Our |N is ACTUALLY infinite> We are restricted to> the domain of terminating decimals.You may be but we are not. > If you cannot understand that,> perhaps a formal argument may help: Assume that we are restricted to> the well-defined set of terminating decimals.Assume we are not.> If you see any evidence> that we should leave that domain, say "stop!". But only if you are> sure.Any function from |N to {0,1,2,3,4,5,6,7,8,9} leaves that domain.And everywhere but in WMytheology such functions exist.For example, the decimal form of 1/3.> > >> > Do you agree that (by presumption) t_i is defined for every i in N?> > Of course! Why not? Isn't every i in N finite?Do you claim that |N is finite? Note that being not finite means being infinite.> >> > I don't want to imagine what you are thinking, because I will risk> > getting it wrong.  I'd prefer that you explicitly give an argument in> > ZF so that we can determine whether it is valid or not.> > In ZF every n in N is finite.But |N is not. And in ZF there is an axiom providing for a set which is not finite.> >> > > Look, presently we work in the system of terminating decimals - by> > > definition. You may be but no one else is. That is one of your your troubles, you claim that everyone makes the assumptions that you make, but that is false.> >> > I don't have any idea what these questions mean> > I know. But it would be nice if you read it again and again.It would be even nicer if you could be clear enough so that Jesse could understand it in one reading. Then maybe others could understand it too.> Or try an> experiment: Write a long sequence of digits d_1, d_2, d_3, ... and do> not stop. Are you in danger to leave the domain of finite sequences?One cannot even write down very large naturals in decimal notation, but that does not mean that they do not exist.So WM is WRONG!--
```