Let $\displaystyle f_{n}, g_{n}$ : R $\displaystyle \rightarrow$ R for n $\displaystyle \in$ N be functions such that $\displaystyle f_{n} \rightarrow f$ and $\displaystyle g_{n} \rightarrow $ g as n $\displaystyle \rightarrow \infty$ uniformly on the set E $\displaystyle \subset$ R, where f, g : R $\displaystyle \rightarrow$ R are functions. Show that $\displaystyle f_{n} + g_{n} \rightarrow f + g $ as n $\displaystyle \rightarrow \infty$ uniformly on the set E.