Date: Mar 25, 2013 6:17 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.


Lets see WM put his argument in a proper the form of the inductive
principle.

I bet he can't!

One acceptable form of induction is:

There exists a set of objects, N, and a zero object such that
1. Zero is one of the objects in N.
2. Every object in N has a successor object.
3. Zero is not the successor object of any object in N.
4. If the successors of two objects in N are the same,
then the two original objects are the same.
5. If a set contains Zero and the successor object of every
object in N, then that set contains N as a subset.
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