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Exercise 1.9 Suppose z = a + bi, w = c + di. Define z < w if a < c, and also if a = c but b < d. Prove that this turns the set of all complex numbers into an ordered set. (This type of order relation is called a dictionary order, or lericographic order, for obvious reasons.) Does this ordered set have the least upper bound property?

Exercise 1.9 Suppose z = a + bi, w = c + di. Define z < w if a < c, and also if a = c but b < d. Prove that this turns the set of all complex numbers into an ordered set. (This type of order relation is called a dictionary order, or lericographic order, for obvious reasons.) Does this ordered set have the least upper bound property?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Exercise 1.9 Suppose z = a + bi, w = c+ di. Define z < w if a < c, and also if a = c but b < d. Prove that this turns the set of all complex numbers into an ordered set. (This type of order relation is called a dictionary order, or lexicographic order, for obvious reasons.) Does this ordered set have the least upper bound property?
Transcribed Image Text:Exercise 1.9 Suppose z = a + bi, w = c+ di. Define z < w if a < c, and also if a = c but b < d. Prove that this turns the set of all complex numbers into an ordered set. (This type of order relation is called a dictionary order, or lexicographic order, for obvious reasons.) Does this ordered set have the least upper bound property?
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