```Date: Apr 5, 2013 4:57 PM
Author: Virgil
Subject: Re: Matheology � 224

In article <560b18fa-164c-4c03-bc3c-2cac32fe9530@j9g2000vbz.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 5 Apr., 12:08, William Hughes <wpihug...@gmail.com> wrote:> > On Apr 5, 11:09 am, WM <mueck...@rz.fh-augsburg.de> wrote:> >> > > On 4 Apr., 23:08, William Hughes <wpihug...@gmail.com> wrote:> >> > > > Nope.  Any single element can be removed.  This does not> > > > mean the collection of all elements can be removed.> >> > > You conceded that any finite set of lines could be removed.  What is> > > the set of lines that contains any finite set? Can it be finite? No.> > correct> > > So the set of lines that can be removed form an infinite set.> >> > More precisely.  There is an infinite set of lines D> > such that any finite subset of D can be removed.> > What has to remain?If one has any set, S, which is order isomorphic to the set of naturals with their natural well-ordering, one can form the family, F, of FISs of that set (finite initial segments).Then any infinite subset of F will union to give the original S but no finite subset of F will union to give back S.That WM seems incapable of comprehending this simple truth marks his as mathematically incompetent.> >> > This does not imply that D can be removed.> > > It does however imply that there is no single element> > of D that cannot be removed. That this does not> > imply that D can be removed is a result that> > you do not like, but it is not a contradiction.> > It is simple mathological blathering to insist that |N contains only> numbers that can be removed from |N but that not all natural numbers> can be removed from |N.Nonsense, Removing any member of |N from |N leaves a proper subset of |N.However, removing FISONs from the set of all FISONs of |N may well leaveenough (infinitely many) to have their union equal |N.Being unable to understand this seems to be WM's personal pons asinorum.> > It is a contradiction with mathematics, namely with the fact that> every non-empty set of natural numbers has a smallest element.> Another wild  false claim by WM made, as usual, without proof.--
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