Definition 1.6.4.label Let $t \ge 0$ and $n \in \nat$, then
\[\floor{t}_{n} = \max\bracs{\frac{k}{n} \bigg |k \in \nat_0, \frac{k}{n} \le t}\]
is the $n$-adic floor of $t$, respectively, and
\[r_{n}(t) = t - \fl{t}_{n}\]
is the $n$-adic remainder of $t$.