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!

--