Let $p_n$ = $(x_n,y_n,z_n)\in R^3$. Show that if ${(p_n)}$ is a Cauchy sequence using metric
$$d(p_j,p_k)=√{(x_j−x_k)^2+(y_j−y_k)^2+(z_j−z_k)^2}$$
then, so are the sequences $(x_n), (y_n), (z_n)$ using the metric
$$d(x_j,x_k) = |x_j-x_k|$$
How can I solve this problem?
Notice that $|x_i - x_j| = \sqrt{(x_i - x_j)^2} \leq \sqrt{(x_i - x_j)^2 + (y_i - y_j)^2 + (z_i - z_j)^2 } = d(p_i, p_j) <\epsilon$