- Your next assignment is due Friday.
- Last time we spent our time on #8 from this section, and discovered some really fascinating things about sequences and subsequential limits. Lindsay encapsulated it by saying that a countable set (a sequence contains at most a countably infinite number of different values) can approach an uncountable number of subsequential limits. Very strange!
For example we saw a sequence whose elements have every natural number as subsequential limits: (1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,....)
For which values are
, where
is a natural number?
- Final comments on material from section 2.2, Subsequences
- Let's check out material from section 2.3, Bolzano-Weierstrass
- Let's begin with a look at the (sketch of the) proof of Bolzano-Weierstrass....
- Then we'll move on to
- #2, p. 58
- #3, p. 58
- #1, p. 58 (proof of Theorem 2-13)