Mathematical induction is a mathematical proof method, which is usually used to prove that a given proposition is valid in the whole (or local) natural number range. Besides natural numbers, generalized mathematical induction can also be used to prove general rational structures, such as trees in set theory. This generalized mathematical induction is applied to the fields of mathematical logic and computer science, and is called structural induction.

In number theory, mathematical induction is a mathematical theorem that proves that any given situation is correct in different ways (the first, the second and the third, all the way down, no exception).

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Mathematical induction proves the key points of solving problems

Mathematical induction has strict requirements on the form of solving problems. In the process of mathematical induction, the first step is to verify that n holds when it takes the first natural number, then assume that n=k holds, and then deduce it based on the conditions of verification and hypothesis. In the following derivation process, n=k+ 1 cannot be directly substituted into the assumed original formula. Finally, summarize the statement.

References:

Baidu Encyclopedia-Mathematical Induction