Nothing very interesting happened this week until yesterday. Two of my classes were canceled on Wednesday for different reasons. That wasn’t very interesting. What was interesting was a grad seminar talk on positive numbers. The topic is not quite as trivial as it sounds. The main question was “Given a ring with a one, how can we tell whether it is possible to separate the ring into two subsets P (for positive) and -P so that the sum of two positives is a positive, the product of two positives is a positive, the union of the two groups is the entire ring, and the intersection is 0?” I was amazed that when he started to talk about ring theory, I actually understood what he was saying! I guess I have spent too much time not understanding what Agboola says about rings.

Cooper mentioned a very interesting problem in topology today: Consider the set S=[0,1]x[0,1]. Now take a countable subset H_1 of [0,1] and let H=[0,1]xH_1. Take another countable subset V_1 of [0,1] and let V=V_1x[0,1]. Does there exist a subset A of S so that for each line [0,1]xh, where h is in the complement of H_1, A covers every point of [0,1]xh except a countable number but for every line vx[0,1], where v is in the complement of V_1, A covers only a countable number of points on v\[0,1]? I know the answer but not a proof, so I probably won’t get any work done this weekend while I struggle with this problem.

I managed to sign up for 2 the 9 (no, I don’t learn from my foolishness) classes I plan to take in the fall today. I need to bug professors for enrollment codes for two of them, see if I can get out of taking a huge stack of prerequisites for another, wait for enrollment codes to be posted in CCS for another, get grad course petitions signed for two others, and fill out a form if I want units for my independent study class. 34 units would be a lot (I’d be surprised if I couldn’t count the number of people at UCSB who plan to take more than that in the fall on one hand), but it doesn’t come close to the CCS record of 63.

Maybe I shouldn’t bother to set an alarm clock tonight. What is the point of being on the verge of falling asleep in my classes? I suppose an alarm clock is a reassurance for me since I’m never convinced that I won’t sleep for 15 hours. But I don’t know what would happen if I didn’t set an alarm clock. I might not get any significant amount of sleep at all since I might worry about not waking up in time for classes. But then I wake up at around 6:00 on weekends whether I like it or not anyway

problem

Either I did not understand the problem or correctly or here is the solution:

By Fubini’s theorem the integral of characteristic function of S over x and then over y is the same as integral over y and then over x. One of the integrals is 1 because we are integrating a function which is 1 a.e., and other is 0 because we are integrating a function is 0 a.e. Contradiction solves the problem.

Re: problem

I meant integral of characteristic function of A.

Re: problem

What is the integral with respect to the product measure? I don’t think Fubini holds here.

How is it possible to take so many units at once?

I go to Berkeley and I have not heard of a single person taking more than 22 units in a semester, EVER.

In the most literal sense, it’s possible to take so many units at once because they don’t stop us. The limit is 95.5 units a quarter, although no one has ever come close to taking that many. I know a few people taking around 30 units a quarter though; it’s uncommon but not unheard of. I take a lot of classes at once because I’m impatient and want to know everything now, and I’m not too concerned about having to work hard. What else am I going to do? I don’t have a social life, and I don’t want one, so I don’t have that excuse. The only thing I could do instead would be to sleep more, but I don’t think I could sleep more than about an extra hour a day even if I tried really hard.