# Definition:Sphere/Metric Space/Radius

## Definition

Let $M = \struct{A, d}$ be a metric space or pseudometric space.

Let $a \in A$.

Let $S_\epsilon \paren{a}$ be the $\epsilon$-sphere of $a$.

In $S_\epsilon \paren{a}$, the value $\epsilon$ is referred to as the **radius** of the $\epsilon$-sphere.

## Linguistic Note

The plural of **radius** is **radii**, pronounced ** ray-dee-eye**.

This irregular plural form stems from the Latin origin of the word **radius**, meaning **ray**.

The ugly incorrect form **radiuses** can apparently be found, but rarely in a mathematical context.

## Caution

It should be noted that the **radius** is not intrinsic to the $\epsilon$-sphere, so that *the radius of a sphere* is ambiguous.

## Sources

*This article incorporates material from sphere (metric space) on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.*