A set is *countable* when it is equinumerous with a subset of $\omega$. This includes all finite sets, including the empty set, and the infinite countable sets are said to be *countably infinite*. An <a href="Uncountable" class="mw-redirect" title="Uncountable">uncountable</a> set is a set that is not countable. The existence of uncountable sets is a consequence of Cantor's observationt that the set of reals is uncountable. ## Uncountability of the reals Cantor's diagonal argument shows that the set of reals is uncountable. ## Uncountability of power sets More generally, the power set of any set is a set of strictly larger cardinality. This article is a stub. Please help us to improve Cantor's Attic by adding information.