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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Laura Maaß,Xiange Zhang,Julian Gansens path; and, in making use of the real number system already in place, we develop real analytic plane geometry using Birkhoff’s axioms of metric geometry. One of the main purposes of this chapter is to explain what is classically known as the Cantor–Dedekind Axiom: The real number system is order-is

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https://doi.org/10.1007/978-3-540-29465-8It is presented here with full arithmetic and historical details, with many identities, and along with its principal, mostly combinatorial, applications including Bernoulli’s derangements. The Division Algorithm for Integers discussed in Section . leads directly to its polynomial analogue, the Divis

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Management im Orientierungsdilemmas and monotonicity) for graphs of polynomial functions using synthetic division applied to difference quotients. We treat the difference quotient of a polynomial as a rational function with a removable singularity at the point where the quotient is taken. Removing the singularity then takes us direc

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978-3-030-75053-4The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Elements of Mathematics978-3-030-75051-0Series ISSN 0172-6056 Series E-ISSN 2197-5604

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https://doi.org/10.1007/978-3-030-75051-0Axiomatic mathematics before calculus; Axiomatic precalculus; Rigorous precalculus textbook; Mathematic