Consider the metric space $\langle \mathbb I,d\rangle$ where $\mathbb I$ is the set of all irrational numbers, and $d$ is the usual distance metric. For each $n\in\mathbb Z^+$, let $x_n =\frac{n + \sqrt 2}{n-\sqrt 2}$. Then:
a. Prove that $\langle x_n\rangle$ is a sequence in $\mathbb I$.
b. As a sequence in $\langle \mathbb I,d\rangle$, prove that $\langle x_n\rangle$ does not converge.
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