 Real-number pairing by separated digits

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 $2\cdot 3^{-k}$ 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.