Definition:Basis Expansion/Termination

Definition
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.

Also see

 * Condition for Termination of Basis Expansion: $\sqbrk {s \cdotp d_1 d_2 d_3 \ldots}_b$ only terminates in certain circumstances.