Definition:Disk/Also defined as

Disk: Also defined as

Many sources define a disk in the context of a general metric space as the set of points within a given distance of a given point.

That is, with the definition that $\mathsf{Pr} \infty \mathsf{fWiki}$ uses for ball.

It needs to be appreciated that when the metric space in question is a Euclidean plane, the two definitions coincide.

In fact, when the metric space in question is the complex plane, the term complex disk is used to mean the ball with the given radious and center.

While all terms are indeed aspects of the same thing, to reduce ambiguity, $\mathsf{Pr} \infty \mathsf{fWiki}$ insists on rigorous consistency in the use of these terms as defined here.