Prove that there exist irrational numbers r and s, such that r^s is rational. Do not use the Gelfond and Schneider Theorem, however, you may g

10. Prove by contradiction that a real number that is less than every positive real number cannot be positive.

Please indicate the method of proof and begin each sentence of the proof on a new line. Result 2 If x and y are positive real numbers, then Jx+y # Vx + Jy . Result 3 There are no positive integers m and n such that m +m +1=n² . Result 4 Prove that 3" > n° for all positive integers n. Result 5 For every real number x +1, 1-x" n-1 1+x+x* +x° +...+x" for all n eN. 1-x

Please, I'm confused on how to do this problem. If it's possible for you to give a some detail on doing it, that'll be great! Thanks!