Tag: completeness

• Completeness of the Real Numbers and Cauchy Sequences: The Absence of GapsFrom the axiom that every bounded increasing sequence converges we derive the Archimedean property, suprema, density, Bolzano-Weierstrass and Cauchy completeness, omitting no steps.MathematicsReal AnalysisUndergraduatecompletenessCauchy sequencessupremumBolzano-Weierstrass theorem~17 min