The Real Numbers and Real Analysis

DOI10.1007/978-0-387-72177-4zbMath1222.26001OpenAlexW364173546MaRDI QIDQ5392149

Ethan D. Bloch

Publication date: 8 April 2011

Full work available at URL: https://doi.org/10.1007/978-0-387-72177-4

zbMATH Keywords

sequencesexponential functionconvergenceuniform convergencecritical pointCantor setpower seriesTaylor seriestrigonometric functioncontinuous functionpolynomial functionpointwise convergencedifferentiable functionlogarithmTaylor polynomialRiemann integralabsolute convergencenatural numbersLipschitz conditionseriesbinomial coefficientsreal numbersintegersMaclaurin seriesmean value theoremsseries of functionsCauchy sequencerational numbersuniformly continuous functionimproper integralprinciple of mathematical inductionDedekind cutintermediate value theoremconditional convergenceRiemann sumordered fieldantiderivativessequences of functionsArchimedean propertyaccumulation pointdecimal expansionderivative of functionl'Hôpital's rulebinomial serieswell-ordering principleinductive setdivergence to infinitylimit of functionintermediate value theorem for derivativesMaclaurin polynomialno gap lemmaPeano PostulatesRiemann-Stielties integral

Mathematics Subject Classification ID

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions (26-01) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics education (97-01) Sequences and series (educational aspects) (97I30) Mappings and functions (educational aspects) (97I20)

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