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?