Description
(Due Mar. 12)
Problem 1 (Exercise 1.5). Let Let −A be the set of all numbers
A be a nonempty set of real numbers which is bounded below. −x, where x ∈ A. Prove that
inf A = − sup(−A).
Problem 2 (Exercise 1.8). Prove that no order can be defined in the complex field that turns it into an ordered field.
Problem 3 (Exercise 2.4). Is the set of all irrational real numbers countable?
Problem 4 (Exercise 2.5). Construct a bounded set of real numbers with exactly three limit points.
Problem 5 (Exercise 2.8). Is every point of every open set E ∈ R2 a limit point of E? Answer the same question for closed sets in R2.
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