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.
: A Powerful and Elegant Method of Proof