Problem Set II

for Tuesday, January 24

Postponed to Thursday, January 26, at Adrian Ioana's office hours.

Section 1.3, page 20:

• Problem 7. Here "explicit" means writing down a straightforward equation for the function.
• Problem 8.
• Problem 9. Support your answers. Clarification: This is what part (a) refers to: Assume that A and B are finite, and classify the set of all functions from A to B. Parts (b) and (c) are similar. The author uses "countable" to mean "countably infinite."

Section 1.4, page 24:

• Problem 7. Use induction.
• Problem 11(c). One method is to do parts (a) and (b) first. There may be easier ways.

Here is an example of a non-Archimedian ordered field.