Definition:Golden Mean Number System/Expansion

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Consider the golden mean number system.

Let $x \in \R_{\ge 0}$ have a representation which includes the string $100$, say:

$x = p100q$

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:

$x = p011q$

The expression $p011q$ is an expansion of $p011q$.

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