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

In article 
WM <> wrote:

> On 24 Mrz., 23:04, Virgil <> 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

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!!