Complete the following questions before our next class.
Exercise 9A questions 1, 2, 3, 5
Complete the following questions before our next class.
Exercise 9A questions 1, 2, 3, 5
Complete the following questions before our next class.
Exercise 8C questions 1–3, 7
Complete the following questions before our next class.
Exercise 8A questions 1ajkl, 2ghi, 6b, 7, 8
Exercise 8B questions 1, 2acef, 5, 6, 7b, 8ac, 9, 10, 12abce, 13, 17
Complete the following questions before our next class.
Exercise 7D.1 questions 1, 3, 6, 7, 10, 12, 18
Exercise 7D.2 questions 3, 5
Exercise 7E 1, 2, 6, 7, 8, 9, 11, 14, 20, 24
Complete the following questions before our next class.
Exercise 7A questions 2, 3, 4
Exercise 7B questions 1cd, 2
Exercise 7C questions 2adeh, 3be, 5abe, 6bfe
Complete the following questions before our next class.
Exercise 6E questions 2bcghi, 3, 4, 5
Complete the following questions before our next class.
Exercise 6D.2 questions 1, 2ad, 4
Complete the following questions before our next class. (Most of this should be review from last year, but if you find any unfamiliar material we can look through that in our next class.)
Exercise 6D.1 questions 2adgj, 4
Complete the following questions before our next class.
Exercise 6C.3 1be, 2ade, 3bc, 4afg
If you’re interested in looking in more detail at the \(\leq\) relation, here’s a fun puzzle to consider.
The real numbers are totally ordered by the \(\leq\) relation, that is, \[\text{(1) for any } a,b \in \mathbb{R},\text{ we have } a \leq b \text{ or } b \leq a.\] We also have the following properties, which are true for any \(a,b,c \in \mathbb{R}\)
\[\text{(2) if } 0 \leq a \text{ and } b\leq c, \text{ then } ab\leq ac, \text{ and}\]
\[\text{(3) if } b\leq c, \text{ then } b+ a\leq c+a.\]
What happens if we try to extend the \(\leq\) relation to the complex numbers? If we can, we would want to do so without “breaking” properties 1–3. Can we extend our ordering relation to the complex numbers without running into trouble in this way?
Complete the following questions before our next class.
Exercise 6C.2 questions 1adg, 2bc, 3, 5aef, 7adef