<P> For an elaboration of this result see Cantor's diagonal argument . </P> <P> The set of real numbers is uncountable (see Cantor's first uncountability proof), and so is the set of all infinite sequences of natural numbers . </P> <P> The proofs of the statements in the above section rely upon the existence of functions with certain properties . This section presents functions commonly used in this role, but not the verifications that these functions have the required properties . The Basic Theorem and its Corollary are often used to simplify proofs . Observe that N in that theorem can be replaced with any countably infinite set . </P> <P> Proposition: Any finite set is countable . </P>

Show that every countable set is a null set