Day 3, Mat420: Real Analysis

Today:

Announcements:
- You have no new assignment: continue working on your homework (and you should have read the first section).
- It might be good to keep a notation page. I'll be introducing a lot of notation (because I'm lazy) that may or may not be the same as our author's, or may not be used by our author.
Today:
- Set operations and the Venn Diagram
  - Union
  - Intersection
  - Complement
  - Set-difference
  How many different regions can one define in the classic venn diagram? A nice Venn diagram applet (for the basic ideas).
- Other set definitions:
  - Subsets
  - Indexing sets
  - Disjoint sets
  - Cartesian product
- One little set proof (11(d)) -- the notion of WLOG
- 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
  - 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 ${A\times{B}}$ , where ${f:A\rightarrow{B}}$
  - Example: the function ${f(x)=\frac{x-1}{x}}$ .
    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?).

Website maintained by Andy Long. Comments appreciated.