```Date: Mar 24, 2013 5:25 PM
Author: Virgil
Subject: Re: Matheology � 224

In article <ea81e7e6-a6f2-422f-89be-b55c2425438a@h7g2000yqi.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 24 Mrz., 10:28, William Hughes <wpihug...@gmail.com> wrote:> > On Mar 24, 10:13 am, WM <mueck...@rz.fh-augsburg.de> wrote:> > <snip>> >> > > Do you agree that the definition "line of the list that does not> > > change the union of all lines" is well defined?> >> > A bit ambiguous.  I interpret it to mean> > " a line of the list, such that if it is removed and> > no other line is removed,> > and all its predecessors are removed tooWhy should removal of one line require removal of any other line at all?Can one not, for example, remove all the even numbered lies without removing any odd numbered lines? This could only be accomplished if one is allowed remove a line without removing all its predecessors.In ZF, one has the set of von Neumann naturals in which each "line" is also a natural, so that the set of naturals is the same as the set of lines. And here the union of the set of all naturals is just the set of naturals. And here the union of ANY infinite subset of the set of naturals is still the set of naturals.But the union of any finite subset of the set of naturals is Not the set of naturals but is merely the maximal natural of that finite set.Note that for any kind of set of naturals, at least when outside Wolkenmuekenheim, a subset is finite if and only if it has a maximal member and a set is infinite if and only if it does not have a maximal member.--
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