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**A Paradox ???**

Consider the following set - ( P(Y) denotes the power set of Y) :

U = { X | There exists a set Y such that X = P(Y)

}

Clearly , U exists :) & is non-empty. Hence, P(U) belongs to U (by the very definition of U).

This contradicts the result by Cantor that the power set always has a higher cardinality than the set - P(U) is a proper subset of U & its cardinality can't exceed that of U.

Is there a flaw in the above argument ? ( I earnestly hope there is !!!).

The above U is not the only set that has this infernal property

- there are others ( consider, for instance, G ={A | A is a set}. P(G) belongs to G.).