Math 554.01 - Analysis I
Test 1 – September 19, 1997
Name:
Directions: To receive credit, you must justify your state-
ments unless otherwise stated. Answers should be provided in
complete sentences.
1 (20pts)
2 (10pts)
3 (15pts)
4 (15pts)
5 (15pts)
6 (15pts)
7 (10pts)
1. a.) Prove (−1)(a) = (−a).
b.) Prove that a > 0 implies (−a)<0.
2. Negate the statement “there exists a positive number δsuch that for each natural number m
there is a natural number klarger than mso that |fk−fm|< δ.”
3. a.) Define countability.
b.) Sketch a proof that the set of rationals numbers is countable.
