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).

Although there is "induction" in the name of mathematical induction, mathematical induction is not a rigorous inductive reasoning method, but a completely rigorous deductive reasoning method. In fact, all mathematical proofs are deductive.

Investigation is one of the most commonly used methods in scientific research. It is a purposeful, planned and systematic method to collect materials about the actual situation or historical situation of the research object.

It comprehensively uses historical methods, observation methods and scientific methods, such as talks, questionnaires, case studies and tests, to make a planned, thorough and systematic understanding of educational phenomena, and to analyze, synthesize, compare and summarize a large number of data collected through investigation, thus providing people with regular knowledge.

Questionnaire survey is the most commonly used survey method, and it is a research method to collect data in the form of written questions, that is, investigators prepare forms for survey items, distribute or mail them to relevant personnel, ask for instructions to fill in answers, and then recycle, sort out, count and study them.