[ionfish]

I'm not saying it's not interesting—in fact, I think it's fascinating—but all of this is implicit in Cantor's Theorem. "Harder question" to me implies there's something there that goes beyond the fundamental result that the powerset of a set X has strictly larger cardinality than X. One might think that it's just harder to understand, but I would dispute that too: if someone thinks they get Cantor's Theorem but has trouble grasping that there is no set of all sets, or largest cardinal number, it just shows that they don't really understand the theorem itself yet.

[pndmnm]

Ah, I gotcha. Yeah, the question as posed is straightforward, though there's some fun stuff (fixed points of ordinal exponentiation, inaccessibles, etc) floating around in the same neighborhood.