Recurring Parts of Multiples of One Thirteenth

Theorem
The multiples of $\dfrac 1 {13}$ from $\dfrac 1 {13}$ to $\dfrac {12} {13}$ can be divided into two sets of equal size:


 * one where the digits of the recurring part consists of a cyclic permutation of $076923$


 * one where the digits of the recurring part consists of a cyclic permutation of $153846$.


 * ReciprocalOf13Cycles.png