yes, I'm pretty sure it's one. If you're talking about a limit, then I recommend Lopital's rule, to rework the problem.

It can't be 1 because 0 in the numerator is the exception to x/x=1.

Undefined of course!

Any finite number, including zero, over zero is undefined.

For example:

1 x 0 = 0
2 x 0 = 0
3 x 0 = 0
...
...
so moving the 0 to the right hand side,

0 / 0 = 1 = 2 = 3 = ...
which is undefined, as 1 obviously is not equal to 2 nor 3 nor anything else.

omg, of course it's undefined

I guess it would be a question over which rule has precedence.

http://en.wikipedia.org/wiki/Division_by_zero

From wikipedia (above link): "These and other similar facts show that the expression 0/0 cannot be well-defined as a limit."

I always liked the idea that anything divided by Zero was infinity. And vice-versa.

...except 0

...and negative numver divided by 0 is negative infinity

0/0 is undefined, but the limit of the function y = x/x at x = 0 is 1. Now chew on that. ;)

Because of the identity property? Aren't all numbers one in that function?

Besides, it obviously has point discontinuity, with the real value placed at infinity.

Found the answer!

http://mathforum.org/dr.math/faq/faq.divideby0.html

"There's a special word for stuff like this, where you could conceivably give it any number of values. That word is "indeterminate." It's not the same as undefined."

"It essentially means that if it pops up somewhere, you don't know what its value will be in your case. For instance, if you have the limit as x->0 of x/x and of 7x/x, the expression will have a value of 1 in the first case and 7 in the second case. Indeterminate."

Infinity is not a number. It is erroneous to state that any expression has a value of infinity.

Fine, it has a value "approaching infinity" happy? For all intents and purposes of rhythm of speech, I claim it has a vlaue of infinity.

Maybe I should start posting all my math assignments on here and having you people give me the answers. This last math class of my life has really straining my interest.

I always liked mathematical theories.

Infinity certainly is not a number, but it's what makes calculus work. That makes it fun. As to my limits comment, I was assuming that he had two expressions that simplified, in the end to 0/0 with substitution.

0/0 is defined and indeterminable in mathematics, or at least it was 25 years ago when I was in college.

oops "as" not "and"

Yeah, the one thing x/0 ISN"T is defined. right?

x/0 is not Infinity. It's undefined. THat's different.

How is that different?
If you divide by infinity, you get zero, and vice-versa. Think about it from a logical perspective: If you divide something infinitley, you'll wind up with nothing.

Dude, that's just the way it is. Smarter people than you and I figured out the difference between infinity and being undefined.

x/0 is infinity (or semantically, approaches infinity) where as 0/0 is indeterminate because any number could be the result. 5*0=0 therefore 5 could equal 0/0. However, 100/0 = infinity there fore infinity * 0 could equal 100 (another indeterminate). This is Algebra 101, not even calculus.

Anything divided by infinity is zero; anything divided by zero is infinity.

The exceptions are ∞/∞ and 0/0, which are both 1.

0/0 is most certainly not 1!

Here's a nice little site I found that may shed some light on the subject:
http://mathforum.org/library/drmath/view/55722.html

abgemacht, I'm doing a math report on it right now, and I've got a book that explains it pretty well. See "Zero, the Biography of a Dangerous Idea", by Charles Seife.

I know 0/0 is not always 1, but it actually is in cases where you are algebraically dealing with imaginary numbers. It's really useful on the a+bi plane.

Would it be correct to assume that 0/0 does not necessarily equal the limit as x approaches 0 of x/x?

Yes.