section	note to yourself the date due	problems
1.1		5a , 11
1.2		1 (Modify the instructions: change Which of the following subsets of AxB to Which of the following subsets of RxR) 6d , 9 , 12 (Note that, since f and g are 1-to-1, the composite g o f is also 1-to-1, and so it makes sense to define the function (g o f)-1 on the range of g o f . You do not need to show this fact.)
1.3		2b , 6 On the base step of Math Induction problems, show that the desired condition is true for the minimum number of k's (or n's or whatever variable you are using) that it is necessary to show that the base step is true.
1.3	just for fun not to hand in	Principle of Mathematical Induction Handout Example 3 , Example 4
1.4		5bdfhj    along with one (and only one) of: 10 , 12 , 15b . Warning: if you are not given that a set is bounded above-and/or-below, you might have to consider different cases which address the different boundedness-vs-nonboundedness. Further instructions: 5: No proofs needed. Pictures are helpful here. To clarify the instructions: Find the supremum and infimum of each of the following subsets of the REAL NUMBERS. 10: Notation hint: Let &alpha = inf A . 12: Show each of the 3 inequalities separately. Also, for each of the 3 inequalities, give an example showing that the inequality can be a strict inequality. 15b: Prove the inequality and also give an example showing that the inequality can be a strict inequality.
1.5		3 (You may use the definition of a rational number but you may not use the fact that the set of rational numbers form a field ... since part of this fact is basically what you need to show), 7 (Hint: the increasing function f(t) = log2 t might come in handy. You may use, without proving, Archimedian's Property.)
1.6		This section is postponed until Section 3.3 since it is not needed until then (see the book's footnote to this section).
1.7
Miscellaneous Exercises		just read through the statements of the exercises