So, math is pretty awesome. It’s my major. Tomorrow I have my second algebra midterm. On the first midterm, I scored 3 points below the mean. I haven’t scored below the mean in years, so I’m kind of pissed. Tomorrow, I hope to redeem myself.
The midterm covers Zorn’s Lemma and Galois Fields, which is some tricky stuff. There’s a lot about algebraic closures. Those are some freaky structures. Especially the algebraic closure of the rationals. Wow, seriously whacked out shit.
Here’s a math joke, as told by Edwin, a crazy kid in my class:
“What’s yellow and equivalent to the Axiom of Choice?
Oh shit, that’s hilarious.
I feel that my math knowledge allows me to say some pretty strange stuff and get away with it. For example, the natural numbers are all the positive numbers without decimal points; 1, 2, 3, etc. Integers are all numbers without decimal points, positive and negative; ... -2, -1, 0, 1, 2…
So, it’s natural to think that there are twice as many integers as there are natural numbers, right? Wrong! There are exactly the same number of integers as there are natural numbers.
Ok, how about rational numbers? Rationals are numbers of the form a/b (a divided by b) where a and b are integers.
There are the same number of rationals as there are natural numbers.
“That’s crazy talk!” you say.
But it’s true. Believe it.
Oh, and how many irreducible polynomials of degree 6 in Z2[x] (Integers mod 2 adjoin x)? Nine. Woot!
All right, I also have two problem sets for economics and probability that aren’t going to do themselves.