```Date: Jan 23, 2013 11:02 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: ZFC and God

On 23 Jan., 14:36, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:> WM <mueck...@rz.fh-augsburg.de> writes:> > I know. But if you have read the discussion, you have seen that two> > matheologians claim just this. Why do they? Because they cannot answer> > the question: What paths are (as subsets of the set of nodes) in a> > Binary Tree that is the union of all its levels? Are there only the> > finite paths? Or are there also the infinite paths?> > Try to answer it, and you will see that you need the omegath level or> > must confess that it is impossible to distinguish both cases. Hence,> > Cantor's argument applies simultaneously to both or to none.>> I'm not interested in the web-published claims of two individuals on a> different topic than we're discussing.You are in error. Pause for a while and think it over.>> Once again, let me remind you what you claimed.  You claimed ZF was> inconsistent, and in particular that ZF proves that the union>>   U_n {1,...,n}>> is both finite and infinite.>> Now, we've had two competing definitions of infinite in this> particular discussion.>> (1) A set S is infinite if there is no natural n such that |S| = n.>> (2) A set S is infinite if it contains a number greater than every> natural n.>> The first definition is what mathematicians almost always mean, and> they *never* mean the second, but this is mere semantics.  Let's talk> results.You are right, mathematicians prefer (1). But matheologians use (2).An infinite set contains a number of elements, at least aleph_0, whichis greater than every finite number.>> We both agree that, using definition (1), the above union is infinite> and (I think) we agree that we cannot show it is finite (=not> infinite).  If I'm mistaken on this point, then please show me.>> On the other hand we both agree that, per definition (2), the union is> "finite", but I have seen no contradiction result, since you have not> shown that the union is "infinite" in this sense.  Nor can you find a> single publication in which a mathematician has claimed the union> above (i.e., the set N of natural numbers) contains an element larger> than every natural.You confuse the things. ZF claimes that the *number of elements* islarger than every finite number. Just this causes the contradiction. Aunion of finite initial segments cannot have a number of elements thatis larger than every finite number.Regards, WM
```