# Defining a ball in mathematics

Which are appropriate phrases to define a ball?

1. Let $B$ be the open ball of radius $r$ centered at $x$.

2. Let $B$ be the open ball of radius $r$ around $x$.

3. Let $B$ be the open ball of radius $r$ about $x$.

4. Let $B$ be the open ball of radius $r$ with the center at $x$.

Or, without \$,

1. Let B be the open ball of radius r centered at x.

2. Let B be the open ball of radius r around x.

3. Let B be the open ball of radius r about x.

4. Let B be the open ball of radius r with the center at x.

Remark I mean a ball in an arbitrary metric space.

• In a math text you wouldn't say "ball", you'd say "sphere". I'm not sure what you mean by an "open" ball. – Jay Aug 29 '14 at 13:45
• @snailplane MathJax is a site-wide setting, and the community needs to justify it with examples of how it would be useful. I doubt it would be enabled for ELL. – 200_success Aug 30 '14 at 5:05
• @Jay Open ball is a technical term for the space within a sphere but excluding the surface of the sphere. – 200_success Aug 30 '14 at 5:08