Proof:
Nothing from nothing leaves nothing
You gotta have something
If you wanna be with me
Nothing from nothing leaves nothing
You gotta have something
If you wanna be with me
I'm not trying to be your hero
'Cause that zero is too cold for me, Brrr
I'm not trying to be your highness
'Cause that minus is too low to see, yeah
Nothing from nothing leaves nothing
And I'm not stuffing
Believe you me
Don't you remember I told ya
I'm a soldier in the war on poverty, yeah
Yes, I am
instrumental break
Nothing from nothing leaves nothing
You gotta have something
If you wanna be with me
Nothing from nothing leaves nothing
You gotta have something
If you wanna be with me
You gotta have something
If you wanna be with me
You gotta bring me something girl
If you wanna be with me
0/0 = indeterminant form. It arises when you have situations as x/e^(-1x) and such. The solution is take the derivative of the denom and the numer and take the limit as x-->0
In the example:
x/e^(-x)
becomes
-(1/e^(-x)) --> 1/0 = infinity.
In the example of x/x -->0
we get 1/1 = 1.
So while we cannot say that 0/0 = anything. We can say that x/x as x approaches 0 (from positive infinity or negative infinity) is 1. Therefore 0/0 might as well be 1. For all intents and purposes differentiation/integration/ etc. It is 1.
Well you can get the value e, 0, infinity, and everything in between when you are taking limits of different sorts of functions that get closer to 0/0, so it doesn't make sense to call it 1.
i only know algebra 1 and geometry.
<---12th grader
Name:
Anonymous2007-01-12 0:05
0/0 = 1, because although under normal circumstances you can't divide something by nothing, you CAN divide something by itself. Therefore the zeros cancel each other out and create one.
In essence, if you can can divide nothing by nothing, you will create.
Name:
Anonymous2007-01-12 0:31
Errrrrr, wrong. 0/0 = ¿, strictly speaking. 0/0 is a limit and you you can only see what it approaches by looking at the whole function.
eg. f(x)=x/x. here as x->0 the function approches it along f(x)=1, so there the limit of 0/0=1
but if it were f(x)=x/x² or f(x)=x²/x etc, the limit will be different. There are many possibilities, who said they even needed to be real?. ¿ is used to show we have insufficient info to give an answer to the limit of 0/0 as it stands.
End of discussion. No bitching about how I am using layman's terms, no "spot the incorrect premise in my circular argument" equations.
End of discussion.
Name:
Anonymous2007-01-12 10:21
anything*0=0
What if "anything" is 1/0?
Name:
Anonymous2007-01-12 10:34
>>29
Such is the power of 0. It nullifies all, even that which defies convetional numeric logic.
Name:
Anonymous2007-01-12 11:50
L'hopital's rule
Winner
Name:
Anonymous2007-01-12 15:10
>>28
[bitching about how your argument is made entirely of fail]
Name:
Anonymous2007-01-12 23:55
Graph f(x)=1/x
Observe
Note: x/0=ANYTHING
Name:
Anonymous2007-01-12 23:58
Funny, I see a hole in the function - a single x for which y has no defined value.
I don't understand how threads like these are allowed to exist.
Okay. Let's say you take the limit of x/x as x approaches 0.
That's simple enough, right? You simplify x/x and get 1, getting lim(x->0)x/x = 1.
Hah, funny. That's not even zero anyway. This is arbitrary anyway, because you will get different values approaching 0/0 with different methods.
lim(x->0) 0/x = 0
lim(x->0) x/0 = null
However, 0/0 still doesn't have any value. The limit of the first example is still 1, but at the actual point (0,1) there is still a hole. Why? Because you can't fucking divide by zero.
Let's maybe take this backwards.
0x0 = 0
That works, sure. However, 1x0 = 0.
Does that mean that 0/0 also equals 1?
2x0 = 0
Or two?
No, this just doesn't mean anything anymore. You can somewhat look at the answer as all values in the complex system, but that doesn't mean anything. Wouldn't it be kinda stupid to endlessly praise someone, no matter what they did, including sitting there, doing nothing? By the same token, it wouldn't be the best approach to look at the answer as all possible values. And it sure as fuck wouldn't be right to look to the answer as zero or one.
Name:
Anonymous2007-01-18 17:20
>>36
Since when can you choose to evaluate a limit based on simultaneously different values of different instances of the same variable? The limit does exist at that point (it is 1 coming from all directions).