this is actually a constructive proof, you are proving that sqrt(2) = a/b implies false and "irrational" is defined as "not rational". A better easy non constr

this is actually a constructive proof, you are proving that sqrt(2) = a/b implies false and "irrational" is defined as "not rational". A better easy non constructive proof is to show that there are two irrational numbers c and d such that c^d is rational. and either c1=d1=sqrt(2) or c2=(sqrt(2)^sqrt(2)) and d2=sqrt(2) as c2^d2 == 2 and if c2 is irrational you are done and if c2 is rational then c1^d1 is rational and you are done. The non constructivity is in that you do not know two irrational numbers c and d such that c^d is rational. In general proving "not P" by "P is absurd" is constructive and proving "P" by "not P cannot happen" is not.