So I am trying to Prove the division algorithm by induction. The Division Algorithm is written in my book as this:
The Divison Algorithm for Natural Numbers If $n$, $m$ are natural numbers and $n\leq m$, then either
There is a natural number $q$ such that $m=nq$, or
There are natural numbers $q$ and $r$ such that $m = nq+r$.
This is what I have so far,
Assume $n$ and $m$ are natural numbers and $n<m$ or $n=m$.
I have no idea how to use induction to prove this theorem. I just need help getting started.