= Real-number pairing by separated digits
{title2=$H:\mathbb R^2\hookrightarrow(0,1)$}
Map each real into $(0,1)$ by a fixed <bijection>, choose its canonical <binary expansion>, and alternate the two bit sequences as ternary digits $0$ and $2$. If two such outputs first differ at position $k$, the leading difference has size $2\cdot3^{-k}$ and the remaining tail has size at most $3^{-k}$, so they are unequal. This gives an explicit <injection> pairing two reals. Iteration encodes every fixed finite real tuple without invoking ambiguous decimal expansions.
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