l^{\infty}=\left\{\left\{x_{n}\right\}_{n \geq 1} \subseteq \mathbf{R}: \sup _{n \geq 1}\left|x_{n}\right|<\infty\right\} \text { Define } d_{\infty}: l^{\infty} \times l^{\infty} \rightarrow \mathbf{R} \text { as followits: for any } x=\left\{x_{n}\right\}_{n \geq 1} \in

l^{\infty}, y=\left\{y_{n}\right\}_{n \geq 1} \in l^{\infty} d_{\infty}\left(x_{2} y\right)=\sup _{n \geq 1}\left|x_{n}-y_{n}\right| \text { Show that }\left(l^{\infty}, d_{\infty}\right) \text { is a complete metric space. }