The strong principle of mathematic induction seemed quite simple, though proposing formulae for recursive functions seem a little difficult. Other than writing out the first few cases and guessing what it might be, then testing it by proof, I'm not sure I see a much better way. I should be excited to learn what other ways there are.
This idea continues to expand our ability to use induction. I like the idea that we can now assume that all elements in a domain from the least element to k can be assumed true in order to prove the implication that the case n = k + 1 is true. As shown in the book, this will become quite useful when dealing with recursive functions.
No comments:
Post a Comment