No: the power set includes a singleton set corresponding to each element of the original set (plus the original set itself and the empty set). (For sets of cardinality > 2 there are, of course, additional subsets as well.) The conclusion (that the power set has greater cardinality than the original set) is still valid, but the (pertinent) elements of the power set are singleton sets, not the “raw” elements of the original set itself.