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1. Introductory ConceptsSet of natural numbers is denoted N, is a collection that people know from the beginning of time. It is the natural numbers people were counting their belongings, counting days. Set of natural numbers is defined as a collection of mostly 1,2,3, 4, ..., but also often treated as 0 integer.2. Designations• n - integer• n + 1 - the successor of a natural number n, each successive formed before the addition of1• 1 is not a successor3. Mathematical InductionMathematical induction is called a certain special way theorem proving. Mathematical induction is closely linked to proving theorems in which the main role is played by the set of natural numbers, but also induction can be used in other areas of mathematics.4. How to prove theorems by mathematical inductionTo prove the theorem by mathematical induction, follow a few steps:I will check the validity of the assertion for the smallest positive integer, that is, for n = 0 or n =1II. Induction assumption: we assume that the theorem is true for any positive integer; n = kIII. Thesis induction: we show the validity of the theorem for the successor of k; n = k +1IV. Proof finish the proposal, which we formulate as follows: assume that the theorem is true for any positive integer k; have demonstrated the validity of this claim for the successor of a natural number k, k +1; Therefore, using the principle of mathematical induction the theorem is true for all numbers belonging to the set of natural numbers.
