Example Countable set The positive rational numbers Q=m/n m, nEN) are countable Proof 11/21/3141/516 212/22/3242/526 3/13/23/33/43/536 4/14/24/3444/54/6 5/1Example Countable Set ◼ The positive rational numbers Q = {m/n | m, n  N } are countable. ◼ Proof: 1/1 1/2 1/3 1/4 1/5 1/6 … 2/1 2/2 2/3 2/4 2/5 2/6 … 3/1 3/2 3/3 3/4 3/5 3/6 … 4/1 4/2 4/3 4/4 4/5 4/6 … 5/1 … …