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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