Date: Mar 22, 2013 5:14 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
On 22 Mrz., 21:33, William Hughes <wpihug...@gmail.com> wrote:

> On Mar 22, 7:21 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> <snip>

>

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

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

>

> Yes, given any set of lines K, every element of K has

> the property that it can be removed without changing

> the union of all lines. Yes, the set of lines that

> has this property is the complete set K.

No doubt.

>

> This is the result of your proof.

>

Given the premise is valid.

> No, this does not mean that one can do something

> that does not leave any of the lines of K

> and does not change the union of all lines.

That is clear because my proof rests upon the premise that actual

infinity is a meaningful notion. I am glad that you have recognized

that.

A ==> B & ~B

implies ~A.

That is basic logic.

> You have not proved,

> and cannot prove the contrary.

> You can only state that it is obvious.

What contrary should I have proved or have intended to prove? I proven

just what you said.

> I know you do not like this result

You are in error. I like just this very result.

> (it cannot

> be true for finite sets)

Of course not. The premise is actual infinity. That is obviously not

possible in finite sets.

> but it is something

> you do not like, not a contradiction.

?

Regards, WM