Definition:Closed Ball/P-adic Numbers/Radius
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Definition
Let $p$ be a prime number.
Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.
Let $a \in R$.
Let $\epsilon \in \R_{>0}$ be a strictly positive real number.
Let $\map { {B_\epsilon}^-} a$ be the closed $\epsilon$-ball of $a$.
In $\map { {B_\epsilon}^-} a$, the value $\epsilon$ is referred to as the radius of the closed $\epsilon$-ball.
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.