Math 131A practice exam Problem 3: Solution We proceed by contradiction: Suppose not. Then A n for all integers n. Put minus on both side of the inequality to obtain A m for all integers m(= n). In other words, the set of all integers Z has an Z upper bou
MATH 131A section 2: Practice Midterm 2. Please write clearly, and show your reasoning with mathematical rigor. You may use any correct rule about the algebra or order structure of R from Section 3 without proving it. Name: Student ID:
1. Suppose (sn ) is
MATH 131A - Practice Midterm 1. Please write clearly, and show your reasoning with mathematical rigor. You may use any correct rule about the algebra or order structure of R from Section 3 without proving it. 1. a) State the Principle of Mathematical Indu
MATH 131A - Practice Midterm 2. Please write clearly, and show your reasoning with mathematical rigor. You may use any correct rule about the algebra or order structure of R from Section 3 without proving it. 1. Suppose (sn ) is a given sequence of nonneg