It seems to me like the more general principle of mathematical induction and the initial statement are so close that the book truly didn't need to distinguish between the do. What I think I'm getting is that for the more generalized statement, your base case doesn't have to be one. So why didn't we just learn that when we introduced it in the first place? It's a fairly simple concept. The toughest part of this section was the algebraic manipulation. I feel like the proofs are much more technical because we are trying to symbolically prove a case each time. This leads to a lot of generally tough mathematics!
For what it's worth I did see the benefit of being able to use a different case than the base case (unless I'm off base on that). As well, the well-ordered principle came into play, which was something I was wondering about from last section. It seems like with induction we can basically prove anything dealing with indexed sets or infinite series. So that's cool.
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