Just a conjecture... If any realizable real is built from the integers, then the single smallest positive real is: 1/aleph-0. See http://mathworld.wolfram.com/Aleph-0.html. In a physical context aleph-0 is finite. Note that there are no positive integers that _exist_ (are realizable) if their value exceeds the number of atomic (in the Democretic sense) particles in the universe.