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of such strings. The dyadic monoid M is then the monoid of all such finite-length left-right moves. Writing as a general element of the monoid, there is a corresponding self-symmetry of the question mark function:

Isomorphism

An explicit mapping between the rationals and the dyadic rationals can be obtained providing a reflection operator

and noting that both and Since is the identity, an arbitrary string of left-right moves can be re-written as a string of left moves only,

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