@ Enlong: no, that's not true.
0/0 is never an asymptote. Get a grapher, and graph f(x)= (x-3)/(x-3). It will be a straight line. Now check out the "table" function of your grapher- at 3, it should say "undefined" or something like that. something/0 makes asymptotes, 0/0 makes undefined.
Whatcha gonna do, little buckaroo? | i be pimpin' madoka ficsYeah, 0/0 is technically 1 but it's an instantaneous displacement. Although my math teacher explained it using a rectangle.
edited 24th Oct '10 5:34:54 PM by Deboss
Fight smart, not fair.0/0 only equals one if it's the limit of a ratio that ends up being 1.
L'Hopital's rule is that if f(x) and g(x) both approach 0 as x approaches c, then lim(x→c) f(x)/g(x) = lim(x→c) f'(x)/g'(x).
the future we had hoped forWe have a rectangle with side lengths a and b. The area of the rectangle is therefore a*b. Now, imagine that b=1/a. So we can now establish that the area of the rectangle is a*1/a or 1. Now substitute 0 or infinity for a. Mind=blown.
Fight smart, not fair.When infinity becomes a real number, the mathematical community will be sure to let everyone else know.
Edit: More seriously, infinity isn't a real number and can't be plugged in. Additionally, 1/x is undefined at 0, so the rectangle can't have length if you plug in 0. (ie It ceases to be a rectangle)
edited 24th Oct '10 11:53:41 PM by Ironeye
I'm bad, and that's good. I will never be good, and that's not bad. There's no one I'd rather be than me.You could argue that 0/0 = 0^(-1) * 0 equals 1, as it WOULD be the definition of 0^(-1), that it is such that it equals 1, but as 0^(-1) doesn't exist in any number system that is relevant (afaik there where some bored mathematicians who constructed a number system where this works) it "technically" is undefined :/
Now everyone repeat: "Undefined".
The area of a rectanle A = a*b, if you want to transform it into b=A/a you have to divide by a, which you can do for every a that is not zero (or infinity if you use a system where it is included). So no, you can't substitute a=0 because your prerequisite for your transformation is a != 0.
@Ironeye
There are projective planes who use R unified with +- infinity as an additional element, but it still doesn't solve the problem with division by zero, as allowing it would always have unwanted consequences.
IIRC that's indeterminate.
However, take any integer n >= 1 but less than infinity though, and you can prove that 1n = 1 by mathematical induction.
Let's see, um, take the base x = 1. So 11 = 1.
Assume that this holds for x = z such that 1z = 1.
Prove that it holds for z+1:
1z+1 = 1z * 11.
Since 11 = 1 and 1z = 1 by the hypothesis, then 1z * 1 = 1 by induction.
This does not hold when n = infinity, by the way, since yeah, indeterminate...
edited 25th Oct '10 7:29:51 AM by MiyuHimegami
@Uchu: Well, yes, I was assuming that we were in Euclidean space and weren't using any extended real number system in place of the standard real line. If one had to use such things, it would push the "proof" out of the realm of the simple and easy to understand.
I'm bad, and that's good. I will never be good, and that's not bad. There's no one I'd rather be than me.1∞ is indeterminate. For example, limx→∞1x=1, but limx→∞(1+1/x)x=e.
edited 25th Oct '10 9:18:47 AM by Ponicalica
the future we had hoped forI tend to think of these 0/0s and 1^infinities as crossroads in the world of math.
edited 25th Oct '10 9:27:06 AM by Longfellow
It Just Bugs MeMy number comments/jokes (that are completely Off Topic):
- 2+2=fish and 3+3=glasses or 8
- Why is it dangerous to do math in the jungle? Add four and four and you get ate
- (completely unrelated to the other comments) Here is a riddle for you: How can you add two single digit numbers together and get a number >18?
- Make sense of this statement:
- 11 was a racehorse
- 22 was 12
- 1111 race
- 22112
edited 25th Oct '10 12:20:02 PM by Belian
Yu hav nat sein bod speeling unntil know. (cacke four undersandig tis)the cake is a lie!

Woah, meta. A thread about Math derails becomes a math derail, with no discussion of the subject at hand.
Charlie Tunoku is a lover and a fighter.