A ball in $\mathbb{R}^k$ given as $ S(a,\rho) = \left\{ x \in \mathbb{R}^k \mid ||x-a|| < \rho \right\} $

Question

Why is it $ S(a,\rho) = \left\{ x \in \mathbb{R}^k \mid ||x-a|| < \rho \right\} $ and not $ S(a,\rho) = \left\{ x \in \mathbb{R}^k \mid ||x-a|| \le \rho \right\} $ ?

$a$ is centrum, $\rho$ is radius.