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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