 The power set of an infinite set \(I\) is not the same size as \(I\) by Cantor’s theorem, is certainly infinite, and so cannot be a set, and so must be the same size as the universe. It follows by usual considerations that the universe is the same size as \(\wp(\omega)\) or as \(\mathbf{R}\) (the set of real numbers, defined in any of the usual ways), and its “cardinal” is \(c\). Further, the first uncountable ordinal \(\omega_1\) is the cardinality of the universe, so the Continuum Hypothesis holds.