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What is the quotient (pseudo)metric $d_\sim$ and how do I identify the infimum of possible sequences in this instance?

Let $Z$ be the the set of dyadic and ternary rationals in the interval $\left[\frac12,1\right)$ whose 3-adic valuation is either $-1$ or $0$, with the standard absolute value topology inherited from ...
Robert Frost's user avatar