Number Theory

    

The Principle of Induction

Authors: Rolando Zucchini

Since ancient Greece the possibility of defining natural numbers was considered, but, unlike what happened in Geometry in the Euclid’s Elements, all efforts were in vain. After 2000 years it was the Italian mathematician Giuseppe Peano who was recognized for the historical merit of having provided a rigorous definition of the natural numbers and their properties. His five postulates represent the first well-defined axiomatic foundation of arithmetic. Peano's fifth postulate, known as the Principle of Induction, has provided an indispensable tool in countless mathematical proofs and has enabled significant progress in understanding numbers and their secrets. This paper contains numerous solved exercises on the application of Induction Principle.

Comments: 17 Pages.

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[v1] 2026-01-22 10:15:17

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