Second mathematical induction

We generally use the first mathematical induction, but the second mathematical induction is often used in the introduction to algorithms, such as 22.4-2 to prove the correctness of the algorithm.

The principle of the second mathematical induction is to establish a proposition related to natural number N. if:

(1) When n = 1, the proposition is true;

(2) assume that when n ≤ k, the proposition is true and n = k + 1 can be properly deduced.

Then, the proposition is true for all natural numbers.

Binary mathematical induction:

It is used to prove the correctness of algorithms in the young table.

When M = 1, for any N, it is true.

Suppose M = K. For any N, it is true.

When M = k + 1,

(1) n = 1.

(2) Assume that n = J is true.

(3) When n = J + 1, it is true.