\begin{definition}[Definition:Basis Expansion/Termination]
Let $b \in \N: b \ge 2$.
Let the basis expansion of $x$ in base $b$ be:
:$\sqbrk {s \cdotp d_1 d_2 d_3 \ldots}_b$
Let it be the case that:
:$\exists m \in \N: \forall k \ge m: d_k = 0$
That is, every digit of $x$ in base $b$ after a certain point is zero.
Then $x$ is said to '''terminate'''.
\end{definition}