Date: Mar 22, 2013 2:43 PM
Author: fom
Subject: Re: Matheology § 224
On 3/22/2013 1:21 PM, WM wrote:

> On 22 Mrz., 16:31, William Hughes <wpihug...@gmail.com> wrote:

>> On Mar 22, 10:05 am, WM <mueck...@rz.fh-augsburg.de> wrote:

>>

>>>> If you want to

>>>> remove all of the lines you have to remove the set of all

>>>> lines that are indexed by a natural number.

>>

>>> But I don't want to remove a set.

>>

>> We have the set of lines. You do not want to leave

>> any of the lines.

>

> I do not want this or that.

> I simply prove that for every line l_n the following property is true:

> Line l_n and all its predecessors do not in any way influence (neither

> decrease nor increase) the union of all lines, namely |N.

>

> This is certainly a proof that does not force us to "remove a set".

> But we can look at the set of lines that have this property. The

> result is the complete set of all lines.

So now you have two complete infinities.

The infinity of objects comprising |N.

The infinity of finite lines whose sequentially

ordered elements are from |N.

Which one is *the* infinity?

Or, if there are many, how do they stand

in relation to one another?