The problem:
Suppose we can reach the first and second rungs of an infinite ladder, and we know that if we can reach a rung, then we can reach two rungs higher. Prove that we can reach every rung using strong induction.
My Question:
In the textbook this problem is from, the solution provided states that for the base cases, we should only assume the fact that we can reach the first rung is the base case and that the fact we can reach the second rung is part of the inductive step.
But, shouldn't being able to reach the second rung of the ladder also be a base case? What makes it not a part of base cases and part of the inductive step?
