**But once we have done that, then taking the example where \(\mathscr{S}\) is universe infinity, the set \(P(\mathscr{S})\) will be an infinite set that is larger than universe infinity. **

Furthermore, we can iterate the process. For any infinite set \(\mathscr{S}\), we construct \(P(\mathscr{S})\), but then we can also construct \(P(P(\mathscr{S}))\), which will be an infinite set larger than \(P(\mathscr{S})\). And \(P(P(P(\mathscr{S})))\) is an infinite set that is larger than \(P(P(\mathscr{S}))\), which is larger than \(P(\mathscr{S})\), which is larger than \(\mathscr{S}\). And on and on. **Thus we will have a never-ending hierarchy of ever-larger infinities.**