Let $C_o(R)$ denote the set of continuous functions on $R$ such that $$\lim_{x\to\infty} f(x)=0$$ and $\lim_{x\to-\infty} f(x)=0$. Prove that $C_o(R)$ is complete in the ||$\cdot$||$\infty$ norm.
I have know idea how to go about this...I think something to do with the limit of Cauchy sequences existing