- Return of the resubmissions of your first assignment.
- Last time:
- Discussion of metrics
- Completeness of the reals (and incompleteness of the rational ordered field)
-
is irrational
- Upper bounds, least upper bounds
- Cardinality -- so far, all infinite sets seem to be the
same size as the natural numbers (
).
- Notice that some of our proofs have required knowledge from other areas of mathematics (e.g. number theory).
- More highlights from Section 1-3.
In particular, we want to look at
- Cantor's diagonalization proof (that the interval (0,1) is too big for the Motel
)
- Theorem 1-15
- Theorem 1-16
- Cantor's diagonalization proof (that the interval (0,1) is too big for the Motel