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

In article 
WM <> wrote:

> On 24 Mrz., 10:28, William Hughes <> wrote:
> > On Mar 24, 10:13 am, WM <> 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 too

Why 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

And here the union of the set of all naturals is just the set of

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