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arXiv · 1811.00877

A One-Sentence Line-of-Sight Proof of the Extreme Value Theorem

Samuel J. Ferguson
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Abstract

We give a one-sentence proof that a continuous real-valued function f on a closed, bounded interval attains a maximum value, by the following device. We define x in [a, b] to be a lookout point if f(t) does not exceed f(x) whenever t lies in [a, x). Letting c be the maximum of the set of lookout points, we prove that f(c) is the maximum value of f.

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BibTeXRIS

Samuel J. Ferguson. 2018-11-04. A One-Sentence Line-of-Sight Proof of the Extreme Value Theorem. https://doi.org/10.4169/amer.math.monthly.121.04.331

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