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Every rational is equal to {$V$} of a finite composition of {$L$} and {$R$} applied to {$(0,1)$}.

Example: {$\frac{43}{19}$}: {$$\frac{43}{19}=2+\frac 1{3+\frac 1{1+\frac 1{3+\frac 11}}}$$} {$$L^2R^3L^1R^3L^1(0,1)=(43,19)\equiv \frac {43}{19}.$$}