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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