Introductory Real AnalysisUniversity of Washington Math 327, Spring 2020 2020, Dr. F. Dos Reis Homework 2 – Key
Exercise 1.The goal of this exercise is to prove that for any positive real number m, the square root of m exists. It means that until the end of the exercise, we cannot use our knowledge about square root of m. At this point we don’t even know the square root exists. Given a positive real numberm, 1. letxandzbe 2 positive real numbers, prove that ifx2< z2 thenx < z.
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2. LetL=xsuch that 0< xandx2 < m. Prove thatLis not empty andLis bounded above.
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3. Letcbe the least upper bound ofL.
(a) Justify the existence ofc.
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Introductory Real AnalysisMath 327, Spring 2020 University of Washington 2020, Dr. F. Dos Reis
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