p1 - . #4. (Problem #4 on p. 23.) Let E be a nonempty...

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Math 5615H: Introduction to Analysis I. Fall 2011 Homework #1 (due on Wednesday, September 14). 50 points are divided between 5 problems, 10 points each. #1. Prove that 6 and 2 + 3 are NOT rational. #2. Let A and B be bounded sets in R . Consider the algebraic sum of A and B , A + B := { x R : x = a + b for some a A and b B } . Show that sup( A + B ) = sup A + sup B . #3. Find sup A, where A := { x R : x 2 < 3 x - 2 }
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Unformatted text preview: . #4. (Problem #4 on p. 23.) Let E be a nonempty subset of an ordered set; suppose is a lower bound of E and is an upper bound of E . Prove that . #5. Represent the complex numbers z 1 = 1 + i 1-i and z 2 = 4 + 3 i 3 + 4 i in the algebraic form z = a + bi with a,b R ....
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