Date: Mar 25, 2013 5:08 PM
Author: Virgil
Subject: Re: Matheology � 224

In article 
<eba0cf26-b31d-4633-9732-a76bf5cc4afe@k4g2000yqn.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 24 Mrz., 23:04, Virgil <vir...@ligriv.com> wrote:
>

> >
> > Induction can prove that something halds for each n in |N, but cannot
> > prove that it holds unambiguously for all n |N.

>
> Induction *creates* the set of all |N, the set that contains the empty
> set and with the set A it contains the next set {A}. That is
> induction! And if you dislike to call it induction, then call it as
> you like, say Hanching, but please understand that my proof then also
> uses Hanching, namely with line n you can remove line n+1.
>
> Regards, WM


While in a union of lines/FISONs, given line/FISON {1,2,...,n+1} in a
union one can remove line line/FISON {1,2,...,n}, if present, without
changing the union but the reverse, which WM claimsabove, is not alwasy
true.

For n = 1, consider the union:
Union{ FISON(n), FISON(n+1) } = Union{{1},{1,2}} = {1,2}.

But removing line n+1 = FISON(n+1) = {1,2} from {{1},{1,2}}
leaves Union{ FISON(n) } = Union{ {1} } = {1}
So removing line n+1 DOES make a difference.

So that even in the simplest of cases,
which even WM certainly should have been able to work out for himself,
WM is clearly and obviously wrong!!
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