Every non-trivial norm on this set is either the standard absolute value or a p-adic norm according to Ostrowski's theorem. This set is the smallest field with characteristic zero. The standard method of proving this set is countable is to consider an infinite square (-5[1])grid (10[2])and to cross out (10[1])repeated elements (10[1])when considering successive diagonals. For showing a number did not belong to this set, Hippasus was supposedly drowned (10[2])by the Pythagoreans. (-5[1])The decimal expansions of elements of this set either terminate or have a repeating sequence. For 10 points, (10[2])name this set denoted by a blackboard Q (10[2]-5[1])which is contrasted with the irrational numbers. (10[1])■END■ (10[2])