[Solution] Prove Theorem 23.6 by justifying the following steps. Suppose that f is not uniformly continuous on D. Then there exists an ε>0 such that,

Question: Prove Theorem 23.6 by justifying the following steps.

Suppose that $f$ is not uniformly continuous on $D$. Then there exists an $\varepsilon>0$ such that, for every $n \in \mathbb{N}$, there exist $x_{n}$ and $y_{n}$ in $D$ with $\left|x_{n}-y_{n}\right|<1 / n$ and $\left|f\left(x_{n}\right)-f\left(y_{n}\right)\right| \geq \varepsilon$

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[Solution] Prove Theorem 23.6 by justifying the following steps. Suppose that f is not uniformly continuous on D. Then there exists an ε>0 such that,

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