- New reading assignment: section 1.2, up to mathematical induction
- You do have an assignment due Friday -- how's that coming?
- Last time:
- How many different regions can one define in the classic venn diagram?
A nice Venn diagram applet (for the basic ideas).
- One little set proof (11(d)) -- the notion of WLOG; it's based on
the idea of symmetry.
- An example composition for figure 1-1, p. 10.
- How many different regions can one define in the classic venn diagram?
A nice Venn diagram applet (for the basic ideas).
- Functions (I hope that I'm not insulting your intelligence, but at
least it shouldn't hurt!):
- Definition and diagram
- 1-1 and onto
- The "obvious" definitions: sums, products, quotients, scalar multiples
- Why functions are so useful:
- Compositions:
Let's think of a pair of functions on the reals, into the reals, that would make each region of the diagram on p. 10 non-empty.
- A function's graph -- subset of the Cartesian product
, where
- Example: the function
.
How can we characterize this function? What do we know about it?
- Inverses
- Let's take a look at Theorem 1-2, and prove part (b) (Problem 17 -- anyone looking at that one?).