Express each positive rational number as m/n, where m, n N and m/n is reduced to lowest
Chapter 10, Problem 10.37(choose chapter or problem)
Express each positive rational number as m/n, where m, n N and m/n is reduced to lowest terms. Letda denote the number of digits in a N. Thus d2 = 1, d13 = 2, and d100 = 3. Define the functionf : Q+ N so that f (m/n) is the positive integer with 2(dm + dn) digits whose first dm digits is theinteger m, whose final dn digits is the integer n, and all of whose remaining dm + dn digits are 0. Thusf (2/3) = 2003 and f (10/271) = 1000000271.(a) Prove that f is one-to-one.(b) Use the Schr oderBernstein Theorem to prove that Q+ is denumerable.
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