Definition:Basis Expansion/Termination
< Definition:Basis Expansion(Redirected from Definition:Termination of Basis Expansion)
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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.