Tag: Intermediate value theorem

• 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 continuityContinuous functionsIntermediate value theoremExtreme value theoremCompleteness~13 min