The use of models in teaching proof by

mathematical induction. En M.

Utilizing (3.67) and by

mathematical induction on [alpha], we arrive at (3.60).

One example of a hands-on, concrete manipulative that can be used actively to develop the concept of

mathematical induction is the Tower of Hanoi problem.

Since the

mathematical induction sets up a claim to X=[eta]>[beta], whereas now has X=g=[beta]+d+[[mu].sub.p]+1> [beta], thus can replace g by [eta], therefore, we have proven that there is a set of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and a pair of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] on the right of [J.sub.[eta]] at No1 [RLS.sub.No1~No[eta]].

Therefore, it is proved by

mathematical induction that the approximated [SINR.sub.L] in (48) is valid for 2 [less than or equal to] q < p.

Since both the basis and the inductive step have been proved, it has now been proved by

mathematical induction that our formula holds for all natural n.

They would like to introduce

mathematical induction, which would allow the computer to make inferences.

That's why

mathematical induction does not apply to an uncountable set.

Here is another example of the use of calculations, due to Dijkstra, which deals with

mathematical induction. Generally speaking, students are taught how to perform

mathematical induction over the natural numbers.

Let k = k + 1; by using

mathematical induction we may find

By (19)-(21), using

mathematical induction, we know (18) holds.

Mathematical Induction: A Powerful and Elegant Method of Proof