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# Let A:= (0, oo) and let k: A-+ R be defined as follows. For x e A, x irrational, we ISBN: 9780471321484 424

## Solution for problem 14 Chapter 5.1

Introduction to Real Analysis | 3rd Edition

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Problem 14

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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ANS 2: Week 4 Notes (4/18) ● Mammary Gland Anatomy ○ Exocrine gland - secretes to outside of body ■ Developmentally like salivary + sudoriferous (sweat) glands ○ Defines the class mammalia ■ Range from skin surface milk patch (monotremes) ■ To variable number of defined glands ○...

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