Definition:Sphere/P-adic Numbers/Center

From ProofWiki
Jump to navigation Jump to search

Definition

Let $p$ be a prime number.

Let $\struct {\Q_p, \norm {\,\cdot\,}_p}$ be the $p$-adic numbers.

Let $a \in \Q_p$.

Let $\epsilon \in \R_{>0}$ be a strictly positive real number.

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


In $\map {S_\epsilon} a$, the value $a$ is referred to as the center of the $\epsilon$-sphere.


Linguistic Note

The British English spelling of center is centre.

The convention on $\mathsf{Pr} \infty \mathsf{fWiki}$ is to use the American English spelling center, but it is appreciated that there may be lapses.