How to teach mathematical induction? Some students are not convinced that a proof by mathematical induction is a proof. I have given the analogy of dominoes toppling but still some remain unconvinced. Is there very convincing way of introducing mathematical induction? I need something which will have an impact. Are there any real life applications of induction?

Have you tried just showing how it works in special cases?
For example suppose you have proved the basis and induction steps for $P(n)$. Now we can show that $P(3)$ holds:


*

*$P(0)$ holds because that's the basis step.

*$P(1)$ holds because $P(0)$ holds and the induction step says that if $P(0)$ holds then $P(1)$ holds.

*$P(2)$ holds because of the induction step and because $P(1)$ holds.

*$P(3)$ holds because of the induction step and because $P(2)$ holds.


Do this for a few cases and you one should see that if you take any $n$ you can always "climb the ladder" from $0$ to $n$ this way.
