Prove that for every pair of expressions in (3.5) there is a positive number b such that the following two statements are equivalent: (i) r is lexicographically smaller than s; (ii) for every choice...

Prove that for every pair of expressions in (3.5) there is a positive number b such that the following two statements are equivalent: (i) r is lexicographically smaller than s; (ii) for every choice of numbers e₁,e₂,. , e_n, such that

r is numerically smaller than s.