I'd like to push our third exam to the 16th of April -- is that
okay?
New assignment:
Wed
3/31
More Infinity
Our poster presentations are coming up at the end
of April (the 26th, 28th, and 30th).
By next Wednesday, 4/7, you should
provide me with a one-page, typed proposal for
your project. You should try to find something
that you're interested in, that also has a
mathematical angle that you can share with your
classmates.
Reminder: Problems pp. 156-161, #2, 6, 7, 8, 13,
20, 37. Due Mon, 4/5.
Today: We continue chapter 3: To Infinity, and Beyond!
Infinity - so mysterious.... but not a number.
Q: Are mathematicians trying to take all the fun out of it by
studying it?! A: Of course not! We relish the mind-blowing mystery. And
there's plenty of fun to be had....
William Blake (from Auguries of Innocence):
To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.
Some things are infinite in size. Maybe it's better to
focus on the adjective than on the noun....
What is a one-to-one correspondence, and how is it useful?
Last time we used a one-to-one correspondence to show that the
set of even natural numbers is the same size as the set of all natural
numbers -- which seems pretty crazy, since the evens are part of all
natural numbers.
II.9, p. 157
Hotel Infinity
Today we'd like to show that the natural numbers are the same size
as the rational numbers, again using a one-to-one
correspondence. This one is a little different, however....
A useful tree....
Next time, we'll show that the irrational numbers are too big for
the natural numbers.
Let's look at another problem:
IV.22
Website maintained by Andy Long.
Comments appreciated.