Date: Mar 22, 2013 5:14 PM
Subject: Re: Matheology § 224

On 22 Mrz., 21:33, William Hughes <> wrote:
> On Mar 22, 7:21 pm, WM <> 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

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