Full Idea
Cantor's Paradox says that the powerset of a set has a cardinal number strictly greater than the original set, but that means that the powerset of the set of all the cardinal numbers is greater than itself.
Clarification
For 'powerset' see Idea 8672
Gist of Idea
The powerset of all the cardinal numbers is required to be greater than itself
Source
report of George Cantor (works [1880]) by Michèle Friend - Introducing the Philosophy of Mathematics
Book Reference
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.113
A Reaction
Friend cites this with the Burali-Forti paradox and the Russell paradox as the best examples of the problems of set theory in the early twentieth century. Did this mean that sets misdescribe reality, or that we had constructed them wrongly?