Tag: Uniform continuity

Limits and Continuity: Reading ε-δ as a Contract on ErrorDirichlet's function shows why 'approaches indefinitely' is no definition. From ε-δ alone we prove uniqueness, the algebra of limits, squeezing, continuity and uniform continuity.MathematicsCalculusUndergraduateLimits Continuity Epsilon-delta Uniform continuity~14 min
Continuous Functions and Uniform Continuity: What It Means for δ Not to Depend on the PointFrom Bolzano-Weierstrass and nested intervals we prove that a continuous function on a closed bounded interval is bounded, attains its extrema and takes intermediate values, then define uniform continuity and prove the Heine-Cantor theorem.MathematicsReal AnalysisUndergraduateUniform continuity Continuous functions Intermediate value theorem Extreme value theorem Completeness~13 min