```Date: Apr 4, 2013 5:01 PM
Author: Virgil
Subject: Re: Matheology � 224

In article <f1f264eb-e018-4e90-98c1-abffa261e23c@gp5g2000vbb.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 4 Apr., 20:57, William Hughes <wpihug...@gmail.com> wrote:> > On Apr 4, 8:30 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> >> >> >> >> >> > > On 4 Apr., 19:45, William Hughes <wpihug...@gmail.com> wrote:> >> > > > On Apr 4, 6:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> >> > > > > On 4 Apr., 18:13, William Hughes <wpihug...@gmail.com> wrote:> >> > > > > > On Apr 4, 5:15 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> >> > > > > > > On 4 Apr., 16:01, William Hughes <wpihug...@gmail.com> wrote:> >> > > > > > <snip>> >> > > > > > > > If you remove "every finite line"> > > > > > > > your are removing an infinite thing> > > > > > > > "an infinite collection of finite things"> >> > > > > > > If an infinite collection of infinite things exists actually, > > > > > > > i.e., IF> > > > > > > it is not only simple nonsense, to talk about an actually > > > > > > > infinite set> > > > > > > of finite numbers, then I can remove this infinite thing because > > > > > > > it> > > > > > > consists of only all finite things for which induction is valid.> >> > > > > > Nope.  The fact that the collection contains only things for which> > > > > > induction is valid, does not mean induction is valid for the> > > > > > collection.> >> > > > > And you believe that, therefore, always elements must exists which in> > > > > principle are subject to induction but in fact are not subjected to> > > > > induction?> >> > > > Nope, just that you can have a collection where everything in the> > > > collection> > > > is subject to induction, but where the collection itself is not> > > > subject to> > > > induction.> >> > > If the collection is something else than all its elements, then you> > > may be right.> >> > No, a collection is no more and no less than "all its elements".> > But an inductive set contains elements that are not subject to> induction?> > > Note the "no less".  A collection need not share a property> > that every one of its elements has.  In this case> > every one of the elements of the collection has the property> > that it can be removed without changing the union.> > The collection does not have this property.> > That is impossible if all elements can be removed.What is true of each separately need not be true of the collection as a collection, so while removeing any one element from a infintie colledtin leaves it infinite , removing all of them does not.At least everywhere other than in Wolkenmuekenheim.Similarly give a set of two element removing any one of them leaves a nonempty set but removing all of them does not. At least everywhere other than in Wolkenmuekenheim.> Compare the collection of three elements.Which collection of three elements? If you man any such set refer to "a set", not "the set" If they are gone, the> collection is empty - you may claim that then there is something> remaining.The empty set remains.> Why do you not think (at least you have not yet mentioned it) that> Cantor's argument also cannot exhaust the complete set?The point of the Cantor argument is that the set in question, the list, is NOT complete!--
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