Through excessive induction, chaotic mathematics can be organized and a large number of mathematics can be systematized. Induction is based on comparison. Through comparison, find out the similarities and differences between mathematics, and then classify the mathematics with the same points into one category, and the mathematics with differences into different categories. Finally, it is proved mathematically.

Extended data:

The principle of mathematical induction can be derived from the following axiom of good order (principle of minimum natural number):

Natural number set is orderly. (Each group of non-empty positive integers has a minimum element); For example, the number of {1, 2,3,4,5} is the smallest-1.

Below we will prove mathematical induction through this property:

For the mathematical proposition that has been proved in the above two steps, we assume that it is not true for all positive integers.

There must be a minimum element k in the set s composed of those invalid numbers. (1 does not belong to the set s, so k >；; 1)

K is already the smallest element in the set S, so k- 1 does not belong to S, which means that k- 1 is true for the proposition-since it is true for k- 1, it should also be true for K, which contradicts the second step we completed. So this two-step proposition holds for all n.

Baidu Encyclopedia-Mathematical Induction