Proof of Non-Uniform Continuity Criteria

Let $A\in\mathbb{R}$ and let $f:A\rightarrow\mathbb{R}$ .
How do you prove the last two statements of the criteria are equivalent?
2 - There exists $\epsilon_0 > 0$ such that for every $\delta>0$ , there exists $x_{\delta},u_{\delta} \in A$ so that $|x_{\delta} - u_{\delta}|<\delta$ and $|f(x_{\delta}) - f(u_{\delta})| \geq \epsilon_0$

3 - There exists $\epsilon_0 > 0$ and there exist sequences $(x_n),(u_n)$ in A such that $u_n - x_n \rightarrow 0$ as $n \rightarrow \infty$ , yet $|f(x_n)-f(u_n)| \geq \epsilon_0$