Abstract
This chapter starts by establishing the natural numbers with the help of Peano’s axioms. Using the axiom of mathematical induction, addition and multiplication of the natural numbers are introduced. In the second part of the chapter, we develop the concept of divisibility of natural numbers. The main result of this part is the proof of the fundamental theorem of arithmetic. The chapter ends with a section on the division with remainder, by means of which the decimal representation of natural numbers is provided. The appendix to this chapter exhibits a selection of deep results and unsolved conjectures on prime numbers such as the Riemann hypothesis and the twin prime conjecture.
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Kramer, J., von Pippich, AM. (2017). The Natural Numbers. In: From Natural Numbers to Quaternions. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-69429-0_1
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DOI: https://doi.org/10.1007/978-3-319-69429-0_1
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