Determining finite value, A rational number r = p/q, where

Determining finite value

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Reference no: EM13129257

A rational number r = p/q, where p, q are in Z, is said to be properly reduced if p and q (q > 0) have no common integral factor other than +1 or -1. Define the function f as follows;

f(x) = q , if x = p/q, properly reduced.
f(x) = 0 , if x is irrational.

Prove that for every real number x, f fails to be bounded at x.

Note: f: A -> B is bounded if there exist a real number M > 0 such that |f(x)| <= M for every x in A.

Reference no: EM13129257

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