taocp - The Art of Computer Programming (2nd ed.): Mathematical Induction

In 1.2.1 Mathematical Induction section, Knuth presents mathematical induction as a two steps process to prove that P(n) is true for all positive integers n: a) Give a proof that P(1) is true; b) Give a proof that "if all P(1), P(2),..., P(n) are true, then P(n+1) is also true";I have serious doubt about that. Indeed, I believe that point b) should be:b) Give a proof that "if P(n) is true, then P(n+1) is also true". The major difference here is that you are only assuming that P(n) is true, not P(n-1), etc.However, these books are old and ha...Read more