Some students wrote the inductive step of their induction "backward" : i.e. they started with what needed to be proven, and arrived to the induction hypothesis, or the definition, after some work. This is confusing because a proof should always start from a true fact to get to the desired conclusion.

In your writeup, you should make the following explicit:

- The statement you are proving
- The method of proof you are using (in that case, induction)
- What your induction hypothesis is, and where exactly you are using it