Hey, a composite anagram wins the day. Huzzah! Thanks all for votes and to geting for hosting and prizes. To be fair to Hilbert, all discussions of his hotel stress "countably infinite" when describing the rooms and guests, so sneaking in an uncountably infinite set is not quite kosher.
After submitting the clue I thought a better surface would be:
Translation of this puzzle in Chinese is incomprehensible
Since composite anagrams are the only place where "the definition must be at the beginning or end" rule can be broken, but it was late and I didn't think the clue had a chance anyway. Shows what I know.