Titlebook: Elements of Mathematics; A Problem-Centered A Gabor Toth Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exclusive lic

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Polynomial Functions,his chapter we return to algebra and study the roots of polynomials, once again with full details of the cubic case. We finish this chapter by the somewhat more advanced topic of multivariate factoring.

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https://doi.org/10.1007/978-3-642-34795-5 are introduced using Peano’s system of axioms. Inherent in the last Peano axiom is his Principle of Induction, one of the fundamental postulates of arithmetic on natural numbers. Among the myriad of applications of this principle, we discuss here the Division Algorithm for Integers along with the g

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Eugenia Larjow,Christian Reuschenbachleads naturally to Dedekind’s original proof of irrationality of the square root of a non-square natural number. As an immediate byproduct, this implies that the Least Upper Bound Property fails. Another advantage of this proof is that it leads directly to the concept of Dedekind cuts, and thereby t

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Informationsmanagement und Controlling, (arithmetic and analytic) properties of these functional limits can be derived by establishing their link with sequential limits. In our largely classical approach, continuity and differentiability of real functions are also introduced and treated here as special limits (stopping short of fully dev