Compact Subset of $\mathbb{R}^n$ is Bounded

Let $n\in\mathbb{N}$, and let $A\subseteq\mathbb{R}^n$. Assume that $A$ is compact in $\mathbb{R}^n$, where $\mathbb{R}^n$ is regarded as a topological space through the topology determined by the Euclidean distance. Then $A$ is bounded as a subset of the metric space $(\mathbb{R}^n,d_E)$.