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. (10[1])The standard method of proving this set is countable (-5[1])is to consider (10[1])an infinite square (-5[1])grid (10[3]-5[1])and to cross out (10[3]-5[1])repeated (10[3])elements (10[2])when considering (10[1])successive (10[1])diagonals. (-5[2])For (10[1])showing a number (10[1])did not (10[1])belong to this (-5[1])set, (-5[3])Hippasus was supposedly drowned (10[2])by the (-5[1])Pythagoreans. (10[1]-5[3])The (10[1])decimal expansions (10[1])of elements of this set either terminate (-5[1])or have a repeating (-5[1])sequence. (10[1])For 10 points, (10[2])name this (10[1])set (-5[1])denoted by (-5[1])a blackboard (10[1])Q (10[2]-5[1])which is contrasted (-5[1])with the irrational (10[2]0[1])numbers. (10[4])■END■ (10[12]0[1])