example of wellfounded induction
This proof of the fundamental theorem of arithmetic^{} (every natural number^{} has a prime factorization^{}) affords an example of proof by wellfounded induction over a wellfounded relation that is not a linear order.
First note that the division relation^{} is obviously wellfounded. The $$minimal elements are the prime numbers^{}. We detail the two steps of the proof :

1.
If $n$ is prime, then $n$ is its own factorization into primes, so the assertion is true for the $$minimal elements.
 2.
Title  example of wellfounded induction 

Canonical name  ExampleOfWellfoundedInduction 
Date of creation  20130322 12:42:23 
Last modified on  20130322 12:42:23 
Owner  CWoo (3771) 
Last modified by  CWoo (3771) 
Numerical id  9 
Author  CWoo (3771) 
Entry type  Example 
Classification  msc 03B10 