This set is due February 25 at the beginning of lecture. Consult the syllabus for details on the homework policy.
1. Show directly that there is no field of elements. (“Directly” means, among other things, that you cannot use the facts mentioned without proof at the end of lecture 4.3.)
2. Construct a field of size Once you are done, verify that all its elements satisfy the equation
3. Solve exercises 36–38 from Chapter 4 of the book.
4. Is the set a field with the usual ?