NationStates Jolt Archive

I'm undecided myself.

Why answer 0?: 0+0=0;0*0=0;0-0=0; all those zeros do look pretty
together. Besides, "from nothingness, nothing comes" (Aristotle)
Why answer 1?: anything divided by itself is 1
Why answer oo?: anything divided by 0 is infinite.

Undefined. You cannot divide by zero.

None of the above. It is undefined.

Undefined. You cannot divide by zero.

Yeah you took that from me. Just ask any TI-83!

Indeterminate.

1/infinity is not 0 so.....

Dividing by zero does not give you infinity. Dividing by zero gives you undefined because it is impossible to differentiate between positive and negative infinity when dividing by zero.

The closer a denominator gets to 0, the closer a number gets to infinity, but so long as the number is not zero, you can differentiate between positive and negative. For instance, 1/(1/4) = 4, 1/(1/8) = 8, etc through 1(1/infinity) = infinity. Why is this? You have 10 apples, if you divide it to 2 groups, they have 5 each, if you divide it to 5 groups, they have two each, but how many groups can you give zero apples to? If you have 10 apples, you can give zero apples to an infinite number of groups.

The closer a denominator gets to 0, the closer a number gets to infinity, but so long as the number is not zero, you can differentiate between positive and negative. For instance, 1/(1/4) = 4, 1/(1/8) = 8, etc through 1(1/infinity) = infinity. Why is this? You have 10 apples, if you divide it to 2 groups, they have 5 each, if you divide it to 5 groups, they have two each, but how many groups can you give zero apples to? If you have 10 apples, you can give zero apples to an infinite number of groups.

I meant either positive of negative infinity.

Numbers will be the downfall of humanity

Anythin divided by zero is undefined.

Therte's a story that Einstein, in one of his great equations, divided by zero accidentally once. Perhaps apocryphal, but still amusing to ponder.

Therte's a story that Einstein, in one of his great equations, divided by zero accidentally once. Perhaps apocryphal, but still amusing to ponder.
I happen to think Einstein was a bit overrated.

The closer a denominator gets to 0, the closer a number gets to infinity, but so long as the number is not zero, you can differentiate between positive and negative. For instance, 1/(1/4) = 4, 1/(1/8) = 8, etc through 1(1/infinity) = infinity. Why is this? You have 10 apples, if you divide it to 2 groups, they have 5 each, if you divide it to 5 groups, they have two each, but how many groups can you give zero apples to? If you have 10 apples, you can give zero apples to an infinite number of groups.


No you can't, since you can't actually give somebody zero of something.

Undefined. You cannot divide by zero.
the motion has been called, seconded, and proved to be so.

jesus people, get a grip...

there's nothing there, and it ain't going anywhere, so there's nothing there... hmm... what's the numerical equivalent of nothing? ZERO

My calculator says:

E

If you have nothing...

and you want to separate it into 0 equal parts....

Wouldnt you have nothing?

Wouldnt the answer be 0?

If you have nothing...

and you want to separate it into 0 equal parts....

Wouldnt you have nothing?

Wouldnt the answer be 0?
As the song so eloquently states...."nothing from nothing leaves nothing". :eek:

As the song so eloquently states...."nothing from nothing leaves nothing". :eek:


You gotta have something, if you wanna be with me.

You gotta have something, if you wanna be with me.
LOL way too funny!!

I happen to think Einstein was a bit overrated.

I smell jealousy....

calculus deals with this. Whatever value your formula has when the numerator and denominator are close to zero can be assumed to be the value of the formula when the numerator and denominator are equal to zero.

In the case of sin[x]/x, you get 0/0 when x = 0. When x is close to zero, sin[x]/x is close to 1, so sin[0]/0 = 1

Deviding a number or non-number (0) by a non-number (0) yields an undefined region because you cannot divide by nothing. The concept of divisable zeros is like negative distance, it doesn't happen.

Raises another question:
You know (hopefully!) that any number to the power of 0 is 1,
So what is 0 to the power of 0?
It obviously can't be 1, because that, as Mr Spock famously said, is illogical. You can't have nothing, raise it by the power of nothing and end up with something.
Actually it's always bothered me, why when you raise a number by the power of nothing you get 1? It just doesn't make sense.

Think about it this way:
Take any number. I'll use 2, as the powers are easy to calculate. 2 to the power of 1 equals 2.
2 to the power of 2 equals 2*2=4
2 to the power of 3 equals 2*2*2=8.
As you can see, when you increase the power by 1, you multiply the previous answer by the original amount (dodgy phrasing, but hopefully you get my drift)

Now do it the other way round.
2 to the power of 3 equals 2*2*2=8
2 squared equals 2*2=4
2 to the power of 1 equals 2.

When the power is reduced by one, the answer is reduced by the original amount.

So when you get to the power of zero, you just divide 2 by 2.
2 to the power of 0 equals 2/2=1.

Hope that made it clear, or at least clearer.

So, that would mean that 0 to the power of 0 is the same as 0/0.

I think it's indetermined.
If 0/0=X
then X*0=0
and we all know any given number multiplied by 0 gives 0, so X can be any given number.

This is maths people, its not open to debate, there is a definate answer and that amswer is :undefined.

Everyone already said it, but it is undefined.

Think about it this way:
Take any number. I'll use 2, as the powers are easy to calculate. 2 to the power of 1 equals 2.
2 to the power of 2 equals 2*2=4
2 to the power of 3 equals 2*2*2=8.
As you can see, when you increase the power by 1, you multiply the previous answer by the original amount (dodgy phrasing, but hopefully you get my drift)

Now do it the other way round.
2 to the power of 3 equals 2*2*2=8
2 squared equals 2*2=4
2 to the power of 1 equals 2.

When the power is reduced by one, the answer is reduced by the original amount.

So when you get to the power of zero, you just divide 2 by 2.
2 to the power of 0 equals 2/2=1.

Hope that made it clear, or at least clearer.

The division thingy is a pretty slipperey slope, as pointed out by Realdorado.
So why not state simply that X^1 (with X=2 in the example) is the previous answer, Y, times X.
X^1 = X = 1*X (this is just part of the definition of ^)
X^1 = X^0 *X (the other part of the definition of ^, with n=1 and n-1=0)
and therefor Y = X^0 = 1.
This works for X=0 too.

Original discussion: division by 0 is UNDEFINED. It has been since the birth of numerical systems.

I think ANY number divided by zero is an undefined number.

It is undefined, The fact is if you devide thngs by zero you end up with illogical answers. 4(2-2)=3(2-2) because they both equal zero devide by (2-2) and tadah 4=3. Since math doesnt want to get into a pile of mush deviding by zero is undefined.

Undefined. Zero is a problematic number so we had to make up some weird rules for it.

The reason why 0^0=1.

Pascal's triangles describes (x+y)^(n-1) where n is the period of the triangle

1-- 1
2-- 1 1
3-- 1 2 1
4-- 1 3 3 1
5-- 1 4 6 4 1

By taking the numbrs and using them as coefficants we get

1-- 1x^0
2-- 1x^1 + 1y^1
3-- 1x^2 + 2xy^1 + 1y^2
ect.


Using the forumula of (x+y)^(n-1) we can use some examples

(5+6)^(3-1)=5^2 +2*5*6+6^2=25+60+36=121= 11^2
ect.

Placing in (2+(-2))^(1-1)=2^0=1 2-2=0 so 0^0=1.

As any Douglas Adams fan knows, the answer is....

42

Now what was the question again?

[QUOTE=Southern Industrial]I'm undecided myself.
"from nothingness, nothing comes" (Aristotle)
QUOTE]

That might not be true. I know this is off subject, but there is a theory of "Spontaneous Generation", pertaining to the matter that caused the big bang. So, from nothingness, something might actually come. Interesting, eh?

Well, in calculus, 0/0 is the indeterminate form, meaning that it doesn't definitely say whatever it is you're trying to find.

Without going into too much detail, it's why
(lim x->3)((x^2-x-6)/(x-3))
cannot be evaluated directly, but you can analytically show that it is 5.