you can list and match up all rational numbers with irrational numbers this way.. lets say i have an irrational number 'c'. Rational->Irrational r1->cr1 r2->cr2 . . . rn->crn There exists an irrational number that is not on this matching, (not equal to any of the crx's) this irrational number can be made by multiplying c to another irrational number 'b' and I can prove that this is not on the list because cb never equals crx because b is irrational and rx is rational is this a valid proof?