Counterexamples in Analysis

Counterexamples in AnalysisThese counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "real variables," starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half,

Natural Number Sequence — Zorn's Lemma

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and the direct method of Liapunov

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Its discussions of formalism and applications move easily between general theory and direct use by offering illustrations of principles to specific cases

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