MAA 4211 Assigment 2
Due date: Friday 9/21/01

• A: pp. 29-31/ 1, 4a (figure out a way to do this that does not require any division computations and does not use a calculator), 5, 8, 9, 10, 11, 13, 14, 15. Hand in only 5,10,11,13,14. Problem 1 uses only material that we've covered as of Friday Sept. 7, and problem 8 uses only that material plus the fact that R is a field; the other problems use material that we will be covering starting Monday Sep. 10.

• B: Read the handout "One-to-one and onto: What you are really doing when you solve equations" posted on the Miscellaneous Handouts page. This relates to what we discussed in class concerning what the process of solving equations has to do with existence/uniqueness issues.

• C: Read the handouts "Peano Axioms for the Natural Numbers" and "Establishing some familiar properties of the natural numbers" posted on the Miscellaneous Handouts page. The second of these has several exercises. You are not required to do the exercises (for now), but at least read through them to get a sense of what one can prove from the axioms. You are also not required to read the proofs in this handout; in fact the proofs would most profitably be read only after you first attempt to prove the theorems (or lemmas, etc.) yourself. However, if you feel that you have not seen good enough examples of proofs in class (where time constraints lead me to be sketchier than is proper for a written proof), you may want to read the examples the handout.

• D: Read the handout "Constructing Z from N". The same comments as above apply.