## Fall 2004

### An Evening "with" R.L. Moore

*Wed., 1 Dec., 6pm*

ACES "XP" room (basement of CRBL)

(or, Math 3341 party for both sections)

Video with
R.L. Moore
"Challenge in the Classroom" plus FOOD (pizza and soft drinks).

### Unsolved problems

None right now.

### What we've done so far

Through Task 46 on page 20.

### What's coming up

For Wed., 1 Dec., be ready for Task 47 on
page 20, and also Exercises 57-60 on page 23 (moving to the new set of
notes, starting Ch. 3). We will be skipping Task 48 and the optional
tasks 49-51. Numbers 52-55 got lost in a renumbering shuffle, and we
will postpone Exercise 56 (and, in fact, make it a Task) until later.

### Homework problems (to turn in)

*Homework 1:* Ex. 2; Ex. 4; Prove 1 + 1/(n^2) converges to 1.

*Homework 2:* Ex. 12; Task 14 (for each, prove your answer carefully and rigorously).

*Homework 3:* Prove (carefully) that sup (0,2) = 2;
prove *Gabriel's Lemma*: If s = sup A, then for all epsilon >
0, there exists an element a of A such that s - epsilon < a =<
s.

*Homework 4:* Task 28 (write it nice!).

*Homework 5:* Exercise 43, part 3.

### Add to your notes

#### Task 21-minus

Let S non-empty,
bounded from above. Then for all epsilon > 0, there exists an element
a in S such that a + epsilon is an upper bound for S.