Can someone give me an example of a bounded function [itex]f[/itex] defined on a closed interval [itex][a,b][/itex] such that [itex]f[/itex] does not attain its sup (or inf) on this interval? Obviously, [itex]f[/itex] cannot be continuous, but for whatever reason (stupidity? lack of imagination?) I can't think of an example of a discontinuous,(adsbygoogle = window.adsbygoogle || []).push({}); boundedfunction for which [itex]\sup\limits_{x\in [a,b]} f(x) \neq \max\limits_{x\in [a,b]} f(x)[/itex].

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# Question related to Riemann sums, sups, and infs of bounded functions

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