April 2nd, 2007

note to self

(no subject)

So it's time for an update. The big thing today? I found out my presentation time for SpARC--that is, I received my official acceptance for my SpARC presentation. I wasn't too worried about this, but getting acceptance things just feels really good. The fun begins at 210E at 9:20am, complete with a post-party at the Scottie Math Bowl, where those other teams are going down. Besides, who doesn't want to hear about astronomy and Internet drama?

This also means that I need to start putting that presentation together, something I keep meaning to start but have never gotten around to. Oops. I should definitely get to that.

What else was special? Oh, that's right, the concert update. That'll have to wait. I'm still taking all of it in, and I still have astronomy class and lab assignments due tomorrow. At least the probability assignment isn't due until Thursday.

Oh oh oh! Guess who finally got a 100% on her number theory assignment. Yes, me. We got them back today, and even though I already knew about it because of Blackboard, I was still excited, especially since I did half of it the day before it was due but still found it easier than the past ones were for some reason after I got pas that block.

I still need to get through my astronomy reading. I figure if I can get through the chapter in the book tonight, then I can read the rest of The First Three Minutes before Thursday and be in good shape since I'm halfway through it now. All I have to say so far is "coooool". Well, if I were more coherent, I'd have more.

Also, excuse me as I spaz out over how little time there is before the end of the semester. Okay, that feels better.

Okay, enough rambling. I'm off to finish the assignment before class tomorrow.
math: coffee to theorems

Math and crushing?

Astronomy class is canceled tomorrow. Sweet. Okay, so Dr. DePree's daughter has the stomach virus, which isn't so sweet, and we still have to do stuff during class time, which Sarah and I are doing tomorrow morning to get out of the way. The verdict is still in the air over the lab.

When I was in the shower, a thought struck me. I was singing along to "Skullcrusher Mountain", one of the songs I mentioned in the soundtrack entry. Then that popped in my mind, along with my commentary to it. And for some really weird reason then I thought of the prime number function. Basically, Pi(n) is the number of prime numbers less than or equal to a natural number n. So Pi(3)=2 (2 and 3 are prime), Pi(15)=6 (2,3,5,7,11,13 prime), and you get the idea.

I then thought of the many unrequited crushes I've had in my lifetime. If I let n be the number of crushes I've had, and let C(n) be the number of crushes (not including celebrity crushes) up to that point, including that one, that have been unrequited, what happens as n -> infinity? More importantly, what happens to C(n)/n? Intuitively, I want to say that C(n)/n -> 1 as n -> infinity because just about all of my crushes have been unrequited. So goes the story of my love life.

But what about those those reciprocated crushes? Let R(n) represent the number of reciprocated crushes up to a number n crushes. Clearly R(n)+C(n) = n because a crush is either reciprocated or unrequited (if a crush is not reciprocated, then we assume it is unrequited). Once again, what happens to R(n)/n as n -> infinity? I want to say this goes to 0. Sure enough, R(n)=n-C(n), so we can replace R(n) with n-C(n). Then:
lim n->infinity (n-C(n))/n
= lim n->infinity (n/n)-(C(n)/n)
= 1-1 = 0

That's assuming my assumption that C(n)/n -> 1 as n -> infinity.

Wow. I guess I really can connect anything to math.
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