PROBLEM SET 2 (DUE IN LECTURE ON SEP 25)
(All Theorem and Exercise numbers are references to the textbook by Apostol; for instance
“Exercise I 3.5-5” means Exercise 5 in section I 3.5.)
Problem 1. Let n be an integer and let x be a real number satisfying n < x < n + 1.
Prove that x is not an integer. (You may assume without proof that the sum
or difference of integers is an integer.)
Problem 2. Do Exercise I 3.12-4.
Problem 3. Do Exercise I 4.10-4. (Binomial coefficients are defined at the beginning of
section 4.10. You can use Exercise I 4.10-3.)
Problem 4. Do Exercise I 4.10-16.
Problem 5. Do all parts of Exercise 1.5-9.
Problem 6. Do parts (a) and (c) of Exercise 1.5-10. (Hint: Consider the polynomial
q(x) = p(x) − 1.)
Problem 7. Prove that 0.999... = 1.
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