Proving Mathematical Induction is Correct

Date: 08/31/2001 at 06:46:52
From: Soh Irene
Subject: How to prove that mathematical induction is correct?

Hi,

I have being trying to prove that mathematical induction is correct. 
I know that I can use proof by contradiction, but I do not know how to 
start.

Irene

Date: 08/31/2001 at 08:13:36
From: Doctor Jerry
Subject: Re: How to prove that mathematical induction is correct?

Hi Soh Irene,

If I understand what  you have said, then I think that the  best reply 
I can make to you is that in many approaches to mathematics in which 
mathematical induction is used as a proof technique, there is an axiom 
guaranteeing this technique. Sometimes the axiom is stated this way:

The set N = {1,2,3,...} of natural numbers has the following property: 
If M is a subset of N for which 1 is in M and n+1 is in M whenever 
m is in M, then M = N.

Proof by mathematical induction is based on this axiom.

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/