Let A:= (0, oo) and let k: A-+ R be defined as follows. For x e A, x irrational, we
Chapter 5, Problem 14(choose chapter or problem)
Let A:= (0, oo) and let k: A-+ R be defined as follows. For x e A, x irrational, we define k(x) = 0; for x e A rational and of the form x = m/n with natural numbers m, n having no common factors except I, we define k(x) := n. Prove that k is unbounded on every open interval in A. Conclude that k is not continuous at any point of A. (See Example 5.1.6(h).)
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