When describing the sizes of sets of objects we find that there are different kinds or sizes of infinities. This video establishes the smallest infinity, the one associated with the counting numbers. A countable set is one that can be placed in a one to one correspondence with the natural, or counting numbers. Georg Cantor (1845 - 1918) showed through diagonalization that the set of all fractions is countable, thus there are as many fractions as there are whole numbers! Part 6 of this series will show that there are sets that are uncountable. Their sizes are larger than the infinity of countable sets, demonstrating that there are different infinities.