Date: Mar 24, 2013 6:04 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 24 Mrz., 10:28, William Hughes <wpihug...@gmail.com> wrote:
> On Mar 24, 10:13 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> <snip>
>

> > Do you agree that the definition "line of the list that does not
> > change the union of all lines" is well defined?

>
> A bit ambiguous.  I interpret it to mean
> " a line of the list, such that if it is removed and
> no other line is removed,


and all its predecessors are removed too

> then the union of all lines
> is not changed"
> This is well defined.
>
> Note that every line has this property.


Of course. And if someone intends to claim that there is any natural
number n such that not l_n including all its predecessors can be
removed, then he should say which that is.

And if he does not know such a nunber but claims that my proof does
not cover all lines, then he sould be able to say what remains beyond
all natural numbers.

> However, there is no information about what will
> happen if you remove more than one line.


See above. Induction (in set theory) holds for all natural numbers
including all predecessors of every natural number.

If there were excemptions then induction would be without any value.

Regards, WM