Titlebook: An Excursion through Elementary Mathematics, Volume I; Real Numbers and Fun Antonio Caminha Muniz Neto Textbook 2017 Springer International

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Induction and the Binomial Formula,tant topic in elementary Mathematics, namely, the .. It will considerably improve our ability of elaborating proofs of mathematical statements that depend on natural numbers. In the other two sections, we shall apply this principle to deduce Newton’s formula for binomial expansion, as well as some i

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Elementary Inequalities,examples of inequalities, for whose derivation we can use the simple mathematics we developed so far. Later, when we have the tools of Calculus at our disposal, we shall return to the study of algebraic inequalities, largely generalizing some of those we will study here.

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The Concept of Function,g the basic concepts of domain, codomain and image, some relevant examples of functions are given. Then, we introduce the notions of monotonicity and extremal values, discussing various examples that, in spite of their elementary character, will reveal themselves to be very useful. The chapter conti

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More on Real Numbers,g other applications, we shall introduce one of the two most important numbers of Mathematics, the number . (as the reader probably suspects, the other one is the number ., which is defined as the numerical value of the area of a circle of radius 1—see [4], for instance). We shall also present a fam

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Continuous Functions,iscussion, we shall present sufficient criteria for a function to be continuous and, among other important results, shall show that every continuous function possesses the .. Also, several interesting examples are scattered throughout the chapter.

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Induction and the Binomial Formula,tant topic in elementary Mathematics, namely, the .. It will considerably improve our ability of elaborating proofs of mathematical statements that depend on natural numbers. In the other two sections, we shall apply this principle to deduce Newton’s formula for binomial expansion, as well as some important related results.