{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw1soln

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

This preview shows pages 1–2. Sign up to view the full content.

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 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}