hw1soln - MATH 410: Homework 1 Solutions Section 1.1 1. For...

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MATH 410: Homework 1 Solutions Section 1.1 1. For each of the following statements determine whether it is true or false and justify (infor- mally) your answer. (a) The sum of irrational numbers is irrational. Solution: False. For example π + ( - π ) = 0. (b) The product of irrational numbers is irrational. Solution: False. For example ( π ) ( 1 π ) = 1. (c) If n is natural and n 2 is odd then n is odd. Solution: True. If n were not odd then it would be even and then so would n 2 . 2. For each of the following statements determine whether it is true or false and justify (infor- mally) your answer. (a) Every nonempty set of real numbers that is bounded above has a largest member. Solution: False, for example [0 , 1). (b) If S is a nonempty set of positive real numbers then 0 inf S . Solution: True. If inf S < 0 then 1 2 inf S < 0 would be a greater lower bound. (c) If S is a set of real numbers that is bounded above and B is a nonempty subset of S then sup B sup S . Solution:
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This note was uploaded on 02/27/2012 for the course MATH 2 taught by Professor Staff during the Spring '08 term at Maryland.

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hw1soln - MATH 410: Homework 1 Solutions Section 1.1 1. For...

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