Cantor's Theorem states that for any set, the size of its power set (the set of all its subsets) is always greater than the size of the original set. This means that you cannot create a one-to-one correspondence between a set and its power set, indicating that some infinities are larger than others.
This theorem was proven by Georg Cantor in the late 19th century and has profound implications in set theory and mathematics. It shows that the set of real numbers is uncountably infinite, while the set of natural numbers is countably infinite, highlighting the complexity of infinite sets.