2. In a remark after the proof of the existence of nonrational numbers, or irrational numbers, it was demonstrated that between any two rational numbers is a rational number and an irrational number. Prove by construction, or by contradiction, that in both cases there are infinitely many rationals and irrationals between the two given rationals. (Hint: For intermediate irrationals, note that for n0m2, we know that ffiffiffi pn B Q, and hence 1ffiffi pn B Q. Note also that 1ffiffi pn ! 0 as n ! y:Þ