Every non-trivial norm on this set is either the standard absolute value or a p-adic norm according (10[1])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 grid (-5[1])and to cross out (-5[1])repeated elements when considering successive diagonals. (-5[1])For showing a number did not belong to this set, Hippasus was supposedly drowned by the Pythagoreans. (-5[1])The decimal expansions of elements of this set either terminate or have a repeating sequence. For 10 points, name this set denoted by a blackboard Q which is contrasted with the irrational numbers. (10[1])■END■ (10[3])