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 (10[1])this set is countable is to consider (-5[1])an infinite square grid and to cross out (10[1])repeated (10[1]-5[1])elements when considering successive diagonals. For showing a number did not belong to this set, Hippasus was supposedly (-5[1])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])