\begin{definition}[Definition:Closed Ball/Real Analysis]
Let $n \ge 1$ be a natural number.
Let $\R^n$ denote real Euclidean space
Let $\left\Vert{\, \cdot \,}\right\Vert$ denote the Euclidean norm.
Let $a \in \R^n$.
Let $R > 0$ be a strictly positive real number.
The '''closed ball of center $a$ and radius $R$''' is the subset:
:$B \left({a, R}\right) = \left\{ {x \in \R^n : \left\Vert{x - a}\right\Vert \le R}\right\}$
\end{definition}