(there are a total of 9 problems):

- (Rudin Ch. 2) #12
- (Rudin Ch. 2) #16
- (Rudin Ch. 2) #17
- (Rudin Ch. 2) #26
- (Bergman (Links to an external site.)) #2.3:1;
- (Bergman (Links to an external site.)) #2,3:3 (assume K is infinite)
- (Problems (Links to an external site.)) X4- either verify that D is a metric or complete the problem as written;
- Let A denote a non-empty bounded subset of the real line. Let s denote the supremum of A. Let e denote a positive number. Use the definition of supremum to prove that there exists a point a in A so that s-e < a.
- Find a bijection between the real numbers and the subset of the real line, (0,1). Prove that your map is injective and surjective.