Today, I was not Christine. I was Janae, the cash register girl at the Sausage Haus.
I think I'll just leave it at that :)
Saturday, October 23, 2010
Tuesday, October 19, 2010
When the earth was split in fives
It's common for my mind to make connections between things I hear in the classroom and eternity, divinity, the universe, etc. And these aren't even theology classes--they're math and science. Well, for a while, it was mostly just the science classes that got me thinking about the divine nature of the universe, about God. But now? I'm in Real Analysis, and oh my goodness, there's some deep stuff in there!
Really, it's fascinating. It's all about numbers so big you can't even imagine, numbers so big that they don't even exist in a definable form. It's about numbers that can get smaller and smaller and smaller but never be nothing. My mind has just been bouncing back and forth between infinite and minuscule, even combining the two concepts at once.
Take this for example: If p and e are both greater than zero, then ne>p for some integer n. In this property, e is considered a very very tiny number, and p is considered a very very large number. So, this is saying that you can always have a number n large enough so that when you multiply it by a tiny tiny number, you will still get a very very large number. There is always something bigger, and there will never stop being anything bigger.
How about this one: Let f(x)={1 if x is rational; 0 if x is irrational}. The rationals and irrationals are both dense in the reals, meaning that in any interval, no matter how small, you can find one of them. So, you get infinitely smaller intervals, all of which have irrationals and rationals in them. In other words, this graph is an infinite number of points at 1 and at 0 with an infinite number of gaps.
I think that's so crazy to think about! This function exists at every point, but it is also discontinuous everywhere. If it were represented physically, it would be both solid and air--present, but made up of holes.
I think numbers are very mystical in nature, and by that, I mean that it's incredible that the structure of the universe is mathematical. I don't mean magical--I ain't no pagan. I mean powerful, full of secrets.
So, this is what my mind does at 10 AM in class.
Really, it's fascinating. It's all about numbers so big you can't even imagine, numbers so big that they don't even exist in a definable form. It's about numbers that can get smaller and smaller and smaller but never be nothing. My mind has just been bouncing back and forth between infinite and minuscule, even combining the two concepts at once.
Take this for example: If p and e are both greater than zero, then ne>p for some integer n. In this property, e is considered a very very tiny number, and p is considered a very very large number. So, this is saying that you can always have a number n large enough so that when you multiply it by a tiny tiny number, you will still get a very very large number. There is always something bigger, and there will never stop being anything bigger.
How about this one: Let f(x)={1 if x is rational; 0 if x is irrational}. The rationals and irrationals are both dense in the reals, meaning that in any interval, no matter how small, you can find one of them. So, you get infinitely smaller intervals, all of which have irrationals and rationals in them. In other words, this graph is an infinite number of points at 1 and at 0 with an infinite number of gaps.
I think that's so crazy to think about! This function exists at every point, but it is also discontinuous everywhere. If it were represented physically, it would be both solid and air--present, but made up of holes.
I think numbers are very mystical in nature, and by that, I mean that it's incredible that the structure of the universe is mathematical. I don't mean magical--I ain't no pagan. I mean powerful, full of secrets.
So, this is what my mind does at 10 AM in class.
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