Diameter of a set

In a metric space $(𝑋, 𝑑)$ the diameter $d i a m (𝑌)$ of a subset $𝑌 \subseteq 𝑋$ is the supremum of the difference between any two points in $𝑌$ , #m/def/anal i.e.

d i a m (𝑌) = s u p {𝑑 (𝑥, 𝑦) : 𝑥, 𝑦 \in 𝑌}

#state/tidy | #lang/en | #SemBr