1, (inductive basis) proves that the proposition holds when n takes the first value n0(n0∈N*);

2. (Inductive recursion) Assuming that n = k (k ≥ n0, k∈N*), it is proved that the proposition is also true when n = k+ 1

The principle of this method lies in: first, prove that the proposition is valid at a certain initial value, and then prove that the process from one value to the next is valid. When these two points are proved, then any value can be deduced by repeatedly using this method.

Extended data

1, induction can be divided into complete induction and incomplete induction. Complete induction is a method to make a general conclusion about this kind of object on the premise of including all of it.

2. Induction and deduction reflect people's thinking modes in two opposite directions, the former is the thinking movement from individual to general, and the latter is the thinking movement from general to individual.

3. Inductive reasoning is a reasoning process from knowing and studying individual things to summarizing and generalizing general laws. In induction and generalization, the interpreter not only uses inductive reasoning, but also deductive method.