I think you're right. I'm badly overlooking a subtlety because I'm narrowing "describe" down to "is a suffix of." But you're right that "describe" can be extended to include a lot of other relationships between parts of the big sentence and little sentences, and you're also right that this argument doesn't necessarily apply if you unconstrain "describe" that way. (I haven't formalized exactly what you can constrain "describe" to mean -- only that there are definitions that obviously make our sledgehammer argument break.)
I think "a sentence can be countably infinite" is implicit from the problem description because the problem implies that our "giant block of descriptions" sentence probably has countably infinite size. (it can't exactly be uncountably infinite)
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