\begin{definition}[Definition:Golden Mean Number System/Simplification]
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 $p011q$.
\end{definition}