Definition:Golden Mean Number System/Simplification
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Definition
Consider the golden mean number system.
Let $x \in \R_{\ge 0}$ have a representation which includes the string $011$, say:
- $x = p011q$
where $p$ and $q$ are strings in $\left\{ {0, 1}\right\}$.
From 100 in Golden Mean Number System is Equivalent to 011, $x$ can also be written as:
- $x = p100q$
The expression $p100q$ is a simplification of $p011q$.
Also see
Sources
- 1957: George Bergman: Number System with an Irrational Base (Math. Mag. Vol. 31, no. 2: pp. 98 – 110) www.jstor.org/stable/3029218