For $X\subset \mathbb{R}^{n}$, consider $X$ as a metric space with metric induced by the usual Euclidean metric on $\mathbb{R}^{n}$. Which of the following metric spaces $X$ is complete?
- $X=\mathbb{Z}\times \mathbb{Z}\subset \mathbb{R}\times \mathbb{R}$
- $X=\mathbb{Q}\times \mathbb{R}\subset \mathbb{R}\times \mathbb{R}$
- $X=\left ( -\pi,\pi \right )\cap \mathbb{Q}\subset \mathbb{R}$
- $X=\left [ -\pi,\pi \right ]\cap \left ( \mathbb{R}\setminus \mathbb{Q} \right ) \subset \mathbb{R}$.
