= Solution
\b[This encoding fails.] Choose two distinct <sets> $0$ and $1$, for example the first two finite von Neumann <ordinals>. The distinct <ordered triples> $(0,0,1)$ and $(0,1,1)$ both encode as
$$
\{\{0\},\{0,1\}\}.
$$
Indeed the repeated <singleton> in the first encoding and the repeated two-element <set> in the second disappear when forming an ordinary <set>. Thus the middle coordinate cannot always be recovered. The issue is loss of multiplicity, not a failure to construct a <set>.
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