8.1.11 Suppose that the set An is denumerable for each n € N We may then list the elements of each set: An anl,4n2, 4n3, 4n4, . . .. Now list the elements of the sets A1, Az, A3, as follows: A1 a11, 412," 013," 414, - Az a21,022, 423, 424, A3 a31,032, 433, 434,Use this construction to prove that U An is a denumerable set: neN This result is often stated, 'A countable union of countable sets is countable.