Definition:Golden Mean Number System/Simplest Form

Definition

Let $x \in \R_{\ge 0}$ have a representation $S$ in the golden mean number system.

Then $S$ is the simplest form for $x$ if and only if:

$(1): \quad$ No two adjacent $1$s appear in $S$

$(2): \quad S$ does not end with the infinite sequence $\cdotp \ldots 010101 \ldots$

Sources

• 1957: George Bergman: Number System with an Irrational Base (Math. Mag. Vol. 31, no. 2: pp. 98 – 110)  www.jstor.org/stable/3029218