Diameter (Metric Space)

Definition

Let $X$ be a metric space with metric $d(\_,\_):X\to X\to \mathbb{R}$.
The diameter of $X$ is the supremum of ${\sup }_{x,y:X}d(x,y)$.

By convention, say diameter of $X$ is $\infty$ when the supremum is not in $\mathbb{R}$.
When the diameter $X$ is in $\mathbb{R}$, say that $X$ is bounded.