## The Real Numbers and Real AnalysisThis text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus. |

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absolutely convergent analog antiderivative axioms calculus courses Cauchy sequence closed bounded interval compute continuous functions Corollary Dedekind cuts deduce defined by f(x denoted derivatives divergent equation exists Extreme Value Theorem f is continuous f is differentiable fact following theorem follows from Exercise function f Fundamental Theorem graph greatest lower bound Hence improper integrals improperly integrable Intermediate Value Theorem interval of convergence intuitive Law for Addition Least Upper Bound Let a,b let f Let g lim f(x limits to infinity logarithm mathematics natural numbers non-degenerate closed bounded notation omit the details open interval ordered field partition of a,b Peano Postulates pointwise polynomial power series present section rational numbers reader in Exercise real analysis real numbers rectangles representative set Riemann integral rigorous special polygon squarable subset Suppose that f Theorem of Calculus uniformly convergent unique Upper Bound Property