The induction principle is a mathematical form of reasoning in which an infinite sequence of propositions follows from a few premises.
Usually, the statements are expressed in form of equalities or inequalities involving Discrete variable  n.

The induction principle is based on a quite clear self-intuitive idea.

Let  Pn  be a sequence of propositions for  n = 0, 1, 2, ….
Assume that the validity of  Pn  implies the validity of  Pn+1. Then it is necessary only to make sure of the truth of  Pn  for any value of  n = k  that results in the truth of  Pn  for any integer  n  ≥  k.

The mathematical induction principle includes the following three constituents:

The induction basis is a true proposition being a starting point for the induction.
In order to form the induction basis it is necessary to find an integer n = k such that the statement  Pk  should be true, that is, we have to make sure of the validity of the proposition in a particular case.
Usually, testing of hypothesis begins with  n = 0  or  n = 1.

The induction hypothesis is an assumption that proposition  Pn  is also true for some integer  n > k.
At this stage of the induction one proves nothing. We only propose a hypothesis, expecting to extend the validity of observations of part of a class of facts over the whole class.

The induction step is the main component of the induction.
Now it is necessary to prove that proposition  Pn+1  follows from proposition  Pn  for  n ≥ k. That is, we proceed from verifications and assumptions to a direct proving of the statement.

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