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Theorem: Continuous Real Functions on Closed Intervals are Uniformly Continuous

Let $[a,b]$ be a closed real interval, $\mathbb R$ be the set of real numbers and \(f:[a,b]\mapsto \mathbb R\) a continuous function. Then \(f\) is uniformly continuous.

| | | | | created: 2017-03-13 20:07:08 | modified: 2017-03-13 20:12:19 | by: bookofproofs | references: [581]

1.Proof: (related to "Continuous Real Functions on Closed Intervals are Uniformly Continuous")

2.Proof: Proof by Contradiction (related to "Continuous Real Functions on Closed Intervals are Uniformly Continuous")

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Bibliography (further reading)

[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983