- You have an assignment due.
- Return of homework (relative to our
overview of infinity.)
- Give an explicit one-to-one correspondence for the figure. What does "explicit" mean?
- Expand
properly using Pascal's triangle.
- Please answer the questions! What happens? Are these formulas any good? Any idea why?
- Does anyone have any "talk reports" to hand in?
- Did anyone get out to the CINSAM event last night?
- Talks and events coming up:
- Friday, 3:05: a Pearson representative will be here to talk about textbook choice for calculus.
- Any other opportunities that you've heard of?
- Whoops! Jen isn't here today, but rather next time.
- Next time: we'll have a visit from Dr. Jennifer Quammen, an alum who went on to graduate school, and eventually veterinary medicine.
- An explicit one-to-one correspondence between the natural numbers and the integers
- An explicit mapping from the natural numbers onto the positive rational numbers (says that there are at least as many natural numbers as there are rational numbers). (See page 14 of our overview of infinity.)
- Cantor showed (by his diagonalization argument) that the real numbers are more numerous than the rational numbers: if we try to put them into one-to-one correspondence, we will fail (he can find a real not "at the dance").
- We can modify Cantor's argument to show that the power set
of a set S -- that is, the set of subsets of the set S --
is always larger than the set itself.
Upshot: this sets up a chain of successively larger infinities!
We'll spend a little time now and then on our projects as we move towards our final project "exposition".
Those who gave me proposals: we're going to partner up and appraise each other's work.
- First time: critique the content on the page, and make positive suggestions for changes
- Second time: critique the writing on the page, and make suggestions for changes