2017•Unpublished venueRequires access
Peano's Axioms
Claudia Menini, Freddy Van Oystaeyen
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Abstract
5.1 We provide an axiomatic introduction of the natural numbers as a totally ordered set. The formal treatment may seem to be boring to the practically oriented student. Nevertheless we hope that the beauty of general theorems like the “Principle of Mathematical Induction” ( Theorem 5.7 ) or the “Recursion Theorem” ( Theorem 5.4 ), as well as the many applications of these, convince the reader of the advantages of a rigorous approach.