Prove that the set $E=\{(x_1, . . . , x_d) :x_1, . . . , x_d>0\}$ in $\mathbb{R}^d$ is not complete by exhibiting a sequence of points $(x_n)_{n \in \mathbb{N}}$ in $E$ that is Cauchy but does not converge to an element of $E$.
I know that $E$ is complete if for every sequence $(x_n)_{n \in \mathbb{N}}$ of points in $E$ that is Cauchy, there exists an $x \in E$ such that $x_n \rightarrow x$. So incompleteness would be that there does not an exist such an $x$. I am not sure how to prove this.
$\{x_n\}$ with $x_n =(1/n , 1/n, \dots,1/n)$.