John Noble (![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
jackofallgeeks) wrote2006-03-21 09:50 pm
jackofallgeeks) wrote2006-03-21 09:50 pm
Binary numbers are so much friendlier...
So, it turns out that I was on the right track hours ago. I scribbled down that there were (p-1)! cycles of length p in S-sub-p, but I couldn't explain *how* that was so. And the math came up funky, because it was choose-4, choose-3, choose-2, choose-1, choose-0, but how can you have choose-0? You have to choose something.
So I looked at p=2 and p=3 and got 1 and 2 p-length cycles respectively and thought, "Hey! Maybe it's p-1 cycles!" So I look at p=5 again and I get the four cycles... and then a fifth pops out. And a sixth. And a seventh. And this isn't right.
The thing is, for our purposes 12345 is the same as 23451 is the same as 34512 is the same as 45123 is the same as 51234. So you peg down the first element and you aren't working with choose-5 at all, you've got choose-4. And it turns out that that lands you (p-1)! anyways!
So now I just drop in an "obviously each cycle has p-1 elements of order-p," because that's what the book told me is the case, wrap that up with my other five proofs, and i'm done with Math!
My brain is getting all over my favorite shirt...
As a note to everyone out there, I really do love math. Like, really really. I was always a math-sci kid in primary school, and through highschool. In college, though, I got two Cs for Calc1 and Calc2 and that scared me away from the higher math -- I so badly wanted to take fun things like number theory and set theory and other theoretical math, but I felt I'd be in over my head. And I still feel like i'm in over my head (hence the goo), but I really love it.
My buddy here, Jodi, has a Master's in Math, and we got to talking about this sort of thing when she came over. We couldn't really get into it, 'cause this is for a take-home final, but I think I'll have to grab her one day and chat about math for a few hours. Cause, I really like it.
So I looked at p=2 and p=3 and got 1 and 2 p-length cycles respectively and thought, "Hey! Maybe it's p-1 cycles!" So I look at p=5 again and I get the four cycles... and then a fifth pops out. And a sixth. And a seventh. And this isn't right.
The thing is, for our purposes 12345 is the same as 23451 is the same as 34512 is the same as 45123 is the same as 51234. So you peg down the first element and you aren't working with choose-5 at all, you've got choose-4. And it turns out that that lands you (p-1)! anyways!
So now I just drop in an "obviously each cycle has p-1 elements of order-p," because that's what the book told me is the case, wrap that up with my other five proofs, and i'm done with Math!
My brain is getting all over my favorite shirt...
As a note to everyone out there, I really do love math. Like, really really. I was always a math-sci kid in primary school, and through highschool. In college, though, I got two Cs for Calc1 and Calc2 and that scared me away from the higher math -- I so badly wanted to take fun things like number theory and set theory and other theoretical math, but I felt I'd be in over my head. And I still feel like i'm in over my head (hence the goo), but I really love it.
My buddy here, Jodi, has a Master's in Math, and we got to talking about this sort of thing when she came over. We couldn't really get into it, 'cause this is for a take-home final, but I think I'll have to grab her one day and chat about math for a few hours. Cause, I really like it.
no subject
no subject
I've since read about the Transfinite (http://24.62.177.166:8080//infin.htm) thing mentioned in that post, and it's fascinating. I mean, how cool is a number that's bigger than infinity?