```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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