Math 3341 Intro to Analysis

Fall 2004

Dr. Duval

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.