Date: Mar 26, 2013 4:17 PM
Author: Virgil
Subject: Re: Matheology � 224
In article

<2dc8b38d-3376-4a6c-89e4-ad4b059d853e@r1g2000yql.googlegroups.com>,

WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 25 Mrz., 23:12, Virgil <vir...@ligriv.com> wrote:

>

> >

> > Lets see WM's statement of the inductive principle.

> >

> Let P(1)

> and let P(x) ==> P(x+1)

>

> Then P(n) at least for every natural number.

>

> Proof: For P(2) follows from P(1), P(3) follows from P(2), and so on.

>

> More is not required.

If proof is not required, or even possible, in any system in which

induction, or some equivalent, is not assumed.

So WM gets a failing grade!

One acceptable form of induction is:

There exists a set of objects, N, and a zero object, 0, such that

1. 0 is a member of N.

2. Every member of N has a successor object in N.

3. 0 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, S, contains 0 and the successor object of every

object in S, then S contains N as a subset.

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