```Date: Jan 24, 2013 8:02 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

On 24 Jan., 13:36, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:> WM <mueck...@rz.fh-augsburg.de> writes:> Well, what you present below is *not* a proof of (*).That is wrong. You have no reason to believe that your definition ofproof is correct or the only one.>>   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?Yes.>> > 4) Certainly you agree that, since all t_i = (t_i1, t_i2, ..., t_in)> > have only a finite, though not limnited, number n of digits, the> > diagonalization for every t_i yields a finite d_i =/= t_ii.> > (The i on the left hand side cannot be larger than the i on the right> > hand side. In other words, "the list" is a square. Up to every i it> > has same number of lines and columns. )>> No idea what you mean by the parenthetical remark.You will have have recognized that here the diagonal argument isapplied. It is obvious that up to every line = column the list is asquare.>> I do agree that d_i is defined for every i in N.  In particular, (d_i)> is an infinite sequence of digits.  Is this what you're claiming, too?> You've lost me.  I don't know what you mean when you say, "everything> here happens among FISs."  And I'm also puzzled by the meaning of the> next sentence.Every t_i is finite. Hence, in a square, if the width is finite, alsothe length must be finite.>> Here are some obvious things.>>   d(j) is defined for every j in N.>   d(j) != 0 and d(j) != 9 for any j in N.>>   Hence the number d does not have a terminating decimal>   representation.Neither the set of t_i does have a largest element. Nevertheless thereis no t_i of actually infinite length.>> This looks like I do *not* agree with your claim that "d cannot be> longer than every t_i".A sequence of squares will never result in a square such that allsides are finite but the diagonal d is infinite. The overlap of d andt_i cannot be larger than t_i.In particular, what would be changed in the length of d if we admittedalso non-terminating t_i (of infinite length)?Regards, WM
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