Is there actually a mathematical rule:

Post Reply New Topic

I am assuming that from the responses, even if you do not think it is important, the little Mom's Law (or rule) hasn't actually been seen before.

0^0 = 1 because everything to the zeroth power is one. Zero to the everything else is zero though, but for some reason 0^0 is different. To be honest I have no idea why. Well, I know what I'm going to be trying to figure out for the next two weeks.

As for the main issue here, it always helps me to remember that (X+Y)^2 = (X+Y) * (X+Y). From there you just have to know to foil that. It always made sense to me to do that.

0^0 is not well defined. it is equal to 0/0 which does not have a well defined value.

however x^0 = 1 for non-zero x. why? x^1/x^1 = 1 but by the law of exponents this is also x^(1-1) = x^0

ruveyn

Random musings: Pondering about infinity
--- Feb 1, 2011 7:30 AM

So, we have no school today. Excited? Sure. Means I get to sleep! But why, then, am I awake at 6:30 in the morning? The world may never know... (But it is really quiet outside. I live on a busy street next to a gas station. The world is dead. On a side note, I think I just heard a transformer explode in the distance. This is goig to be a fun storm.)

After reading the comments on the quiz, I was thinking about the concept of infinity. In my head, I understand and can imagine it, but explaining it is impossible. It makes my brain hurt, but I like things like that. I am a thought massochist. Anyway, what is infinity? Forget text book definitions for a minute. What do you feel infinity really is? In my calculus class, we just call it "really big" or "really small." But how can we really place a limitation like that on infinity? It is endless and beginningless, but it is not. To me, big is big, but infinity would be bigger than big. I seem to imagine a huge something filled with a large quantity of something else. There is an open end, and the largest amount of "stuff" I can imagine is filled to the brim - there can be no more added. Infinity is more added (where it is spilling out and you can not see where it stops). But this is just for large infinity. There is small infinity as well. To me, that is harder to imagine. It is so small, there is nothing, but there is not "nothing," there is still something, but if there is something, then it can still be smaller and there can never be nothing, although that's what infinity is - the unattainable goal. Then there is infinity in general. It contradicts itself. It is beyond the largest of large and the smallest of small all at the same time.

But then there is the problem of expressing it as a quantity in the first place. Infinity is not a number, but at the same time, it is. It is like a number on steroids, or maybe LSD. What kind of number can have a starting point, no starting point, be cut in half and doubled while still remaining the same? Just think for a second. Half of really big is really big, and twice really small is still really small... smaller, even. How about this: Can infinity be both huge and tiny at the same time? It breaks all the rules and concepts about mathematics that we know. It is even stranger than chaos (although Mandelbrot Sets rule).

It infinity was a physical thing, then it couldn't exist in our universe. It would break all the physical laws of the universe as we know them. Our universe is set up to follow parameters, but infinity does not follow any, except to say that it "is." It takes rules and throws them out of the window (reminds me of a rebellious teenager). Subatomic particles follow rules, even if they are a different set of rules (I am sure to get comments on this one). For those particles that we are now discovering that seem to defy physics, I am sure that their explanation will be found. For now, they are a curiosity.

To me, trying to imagine the concept of infinity is like trying to think of what is, or was, before time began. We live in a universe where time "is" (just like infinity "is"), and no time can not be explained without using temporal words. Our language lacks the means to describe such things as "no time" or infinity. That doesn't mean that it can't be, but it can't. Can it? Just because we can't imagine or describe something, does that mean it is impossible?

Infinity does not actually exist. It is not a thing. It is just a concept that we use to describe things, but then again, isn't that all number are as well?

when they would tell us that if it said 0/0, we had to stop and say no solution,

My daughter (who is typically very good at math) has always been confused about not "distributing" powers into a binomial (x + 2)^2 is (x + 2)(x + 2) not (x^2 + x^2).

It's because zero is not well defined. It is more than nothing.

Do you mean (x^2 + 2^2)? but theres a theorem that states that (x+2)^2 is [X^2 + 2^2 + 2(x)(2)] right? because when you expand (x+2)^2 it is (x+2) multiplied with itself, but not raising what's inside the brackets to the power of 2.

zero is very well defined. Try 1 - 1.

Sometimes in math there really is no solution.

My daughter (who is typically very good at math) has always been confused about not "distributing" powers into a binomial (x + 2)^2 is (x + 2)(x + 2) not (x^2 + x^2). She knew it shouldn't be done, but for her, if she does not have a reason, she does not fully understand (like the discussion we had yesterday of why 0^0 = 1). I finally ended up telling her this, but I don't know if there is actually something out there that states this.