whether there exists any example of a continuous and a bounded function which is not Lipschitz continuous?
2026-03-27 19:30:59.1774639859
example of a continuous and a bounded function which is not Lipschitz continuous
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$x \mapsto \sqrt x$ on $[0,1]$ is such a function. If it were $M$-Lipschitz, then for all $x,y \in [0,1]$ with $x \neq y$,
$$\sqrt x + \sqrt y \ge \frac1M$$
Which is a contradiction.