Full Idea
Inductive proof is not guaranteed to work in all cases and, particularly, it depends heavily on the choice of the ordering.
Gist of Idea
Inductive proof depends on the choice of the ordering
Source
Michal Walicki (Introduction to Mathematical Logic [2012], 2.1.1)
Book Reference
Walicki,Michal: 'Introduction to Mathematical Logic' [World Scientific 2012], p.69
A Reaction
There has to be an well-founded ordering for inductive proofs to be possible.