Necessary and Sufficient Conditions for Integrability
Every continuous function [a,b] →ℝ is uniformly continuous. There are three natural proofs of this theorem, using (a) The Nested Interval Theorem, (b) the Heine-Borel Theorem, and (c) the Bolzano-Weierstrass Theorem respectively.
KeywordsContinuous Function Limit Point Differentiable Function Bounded Function Open Interval
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