how wrong would a proof be

I'm given some ideas of how a induction "traps" is raised by today's lecture. As to me, this happens that i write down the proof before convincing myself that each step follows the previous steps rigorously. We know that there are base case, induction hypothesis and induction step in a formal induction proof. The subtle may be made by missing one of them or by saying something that mismatching the fact. I sometimes make mistakes by making implicit assumption, and the result is that i couldn't reach the conclusion since it is incorrect at the beginning. To understand the statement is also important since the predicate is chosen from the statement. For the last problem on assignment 1, we should carefully remain the property of a ternary tree when we make our assumption. Good luck for the assignment 1.