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. Mathematical induction is a completely rigorous deductive reasoning method. In addition to natural numbers, it can also be used to prove the general well-structured structure in a broad sense, which can be applied to the fields of mathematical logic and computer science, called structural induction, such as trees in set theory.
Solving problems by mathematical induction
The simplest and most common mathematical induction is to prove that a proposition holds when n is equal to any natural number. Prove that the proposition is true when n= 1 Assuming that the proposition holds when n=m, it can be deduced that the proposition also holds when n=m+ 1
(m stands for any natural number) 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. It may be easier to understand this method by thinking of it as domino effect.
For example, you have a long list of upright dominoes. If you can: prove that the first domino will fall. It is proved that as long as any domino falls, the next domino adjacent to it will also fall. Then it can be concluded that all dominoes will fall.