# 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