I know this sounds kind of like a basic question, but why does the method of mathematical indcution work to prove things like sequences and such? All the other proof methods I have learned have made sense to me, and I can prove using logical truth tables or axioms, but I don't really get how this method works. Is there some special axiom I don't know about, or is there perhaps a proof that proves the method works? My problem is not applying it, but understanding exactly how the steps I am taking prove whatever it is I am doing. I can apply it and prove things with it, but I would really like to know exactly what it is I am doing in proving a base case, assuming for n, and then proving for n+1. Thanks in advance for answer to this question. I know it is kind of basic, but it didn't really fit the format for the Homework subforum.