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# what is 0 divided by 0?

what is 0 divided by 0?
0.  24%  [ 19 ]
infinity.  25%  [ 20 ]
1.  6%  [ 5 ]
chuck norris.  42%  [ 33 ]

MarzEz
what is 0 divided by 0?
does anyone know?
well, technicaly it could be any of the following:
0, because 0 divided by anything is 0.
infinity, because anyhting divided by 0 is infinity.
1, because anything divided by itself is 1.
chuck norris, because he feels like it. http://www.chucknorrisfacts.com/
i personally think it's chuck norris, but my second option is 1.
molif
who do he think he is..? he can be dvided by zero..?
Sephy22
At first I think I would go with 0. But that I think of it, though my thinking might be dangerous, it could possibly be 1..
Then again I'm really leaning towards the whole Chuck Norris thing. cause he invented water. :/
actually, 0 / 0 can be both 1 and infinity.

i cannot remember the exact thing, and even if i remember, i don't think i can explain it here.

it was when i learned about

lim (x -> 0) (f(x)/g(x))

that we discuss when x approaches 0, f(x)/g(x) can both be 1 or infinity.

but then again, i need to ask chuck norris if he'll agree with it.
Afaceinthematrix
 badai wrote: actually, 0 / 0 can be both 1 and infinity. i cannot remember the exact thing, and even if i remember, i don't think i can explain it here. it was when i learned about lim (x -> 0) (f(x)/g(x)) that we discuss when x approaches 0, f(x)/g(x) can both be 0 or infinity. but then again, i need to ask chuck norris if he'll agree with it.

Ummm.... no. 0/0 will be undefined, it is not one. I think you may have misunderstood the concept of limits. According to what you said, the lim (x -> 0) ((4x)/x) will be one instead of four. So theoretically, based on what you said, you can make the limit as x approaches zero of anything one by multiplying the top and bottom of a fraction by x. So I'd say that you either misunderstood limits or I simply didn't understand what you were trying to say.
mattyj
Its infinity, because Chuck Norris said so
leontius
I think it is undefined. Division is basically how you divide a piece into multiple pieces. So 1/0 means, "I have 1 piece of cake, how much does 0 person will have if I share it equally?" The answer is undefined because there is even no person in the first place. That is also the same for 0/0.

(Now that I think about it, that person may have infinity pieces of cake, but we won't even be able to know that)
the-guide
It's an unreal equation -- no reality in reality but infinity in theory.
Coen
According to the rules of math, it can be both 1 and infinity as is said here before. I'd go for the not existing option that you shouldn't try to solve this as it has no use anyway
ashok
 the-guide wrote: It's an unreal equation -- no reality in reality but infinity in theory.

Same in my opinion...
MarzEz
Leontius's awnser made me rethink my awnser...
if you have 0 pieces of cake, and 0 pieces to give to people, then no-one gets any cake, therefore the awnser is 0.
except chuck norris. he gets cake, even though there isn't any. so technically, that makes the answer 1.
although, there's only no cake if your experiments are too successful. (see Portal, the game.)
Afaceinthematrix
 MarzEz wrote: therefore the awnser is 0.

No, it is not 0. It is undefined. The answer is not one or zero. The answer is undefined! You cannot ever divide by zero because the answer is so infinitely great that it cannot be defined by numbers.
Gieter
If you divide by 0, the universe will collapse. At least that's what they teached me in math classes.
rvec
 Gieter wrote: If you divide by 0, the universe will collapse. At least that's what they teached me in math classes.

Well at least php does
 Quote: Warning: Division by zero in /var/www/null.php on line 2
vineeth
Well, to answer this question, we must think a bit philosophical also. First lets define ZERO and the process of DIVISION
Afaceinthematrix
 vineeth wrote: Well, to answer this question, we must think a bit philosophical also. First lets define ZERO and the process of DIVISION

This isn't a philosophical question at all. It's a simply arithmetic problem at an elementary level. 0/0 = undefined.
snowboardalliance
There's no option for undefined in your poll but that's all 0/0 is. or x/0
Afaceinthematrix
 snowboardalliance wrote: There's no option for undefined in your poll but that's all 0/0 is. or x/0

There was sort of an option. Infinity was an option, and in this case, infinity more or less means the same thing as undefined. The reason why something divided by zero is undefined is because it's too infinitely great to be defined by numbers.
Sundae
no, x/0 is undefined, not because the number is too large
some guys in the past apparently write undefine using infinity symbol
but undefined is still undefined, not infinity
carlospro7
this is what happens when you divide anything by 0:

Zombie
ROFL to carlospro7, nice pic... did you photoshop that? Anyway 0/0 is undefined... it doesn't take a genius.
Afaceinthematrix
 Sundae wrote: no, x/0 is undefined, not because the number is too large some guys in the past apparently write undefine using infinity symbol but undefined is still undefined, not infinity

1/0 is undefined because the value will be too great to define with numbers. However, saying that the answer is infinity isn't proper.
bloodrider
None of the poll options are correct, although I was tempted to answer Chuck Norris, remembering him singing the theme "When the eyes of the ranger are up on you..." almost causes me an "division by zero" error on my brain

 Afaceinthematrix wrote: 1/0 is undefined because the value will be too great to define with numbers. However, saying that the answer is infinity isn't proper.

Anything divided by zero it's an indetermination, the result of that kind of division won't be a small number or a big number, it simply doesn't exist
BPrice
for 0/0 its got to equal 0

If you want to get technical on this issue what would the other sums be.

0+0=
0-0=
0x0=

I think all is zero but what do you think?
Nameless
The answer to zero divided by zero is OH SHI-

Everybody knows that!
Stevezorr
You can't divide by zero. It's as simple as that.

You do not want to blow-up the universe, do you?
Afaceinthematrix
 BPrice wrote: for 0/0 its got to equal 0 If you want to get technical on this issue what would the other sums be. 0+0= 0-0= 0x0= I think all is zero but what do you think?

It's not zero. It's undefined. It's not a matter of what you think, it's a matter of fact.

bloodrider wrote:
None of the poll options are correct, although I was tempted to answer Chuck Norris, remembering him singing the theme "When the eyes of the ranger are up on you..." almost causes me an "division by zero" error on my brain :lol:

 Afaceinthematrix wrote: 1/0 is undefined because the value will be too great to define with numbers. However, saying that the answer is infinity isn't proper.

Anything divided by zero it's an indetermination, the result of that kind of division won't be a small number or a big number, it simply doesn't exist :!:

The reason that it doesn't exist is because the value is too infinitely large to be defined by numbers.

Look:

1/1 = 1
1/2 = 1/2
1/3 = 1/3
1/4 = 1/4
.
.
.
The larger the number that you divide by gets, the smaller the value gets.

Likewise:

1/(1/2) = 2
1/(1/3) = 3
1/(1/100) = 100

The smaller that that number gets, the larger the product will be. So by the time you get to zero, you will have a number too infinitely large to define because if you define it as, let's say 1000000, then someone can simply say that that's incorrect because 1/(1/1000000) is 1000000, and by definition, 1/1000000 is larger than zero so the result needs to be smaller. That's why the number doesn't exist. It's too infinitely large to be defined by numbers. However, saying that x/0 = infinity (like someone mentioned earlier) isn't proper because there's a difference between infinity and infinitely large.

Edit:

I just thought of another way to explain my point. Think of division as repeated subtraction. Take any number (let's just use 20/5) and 5 until you get 0.

1. 20-5=15
2. 15-5=10
3. 10-5=5
4. 5-5=0

We did that 4 times, therefore the answer is 4.
20/11
1. 20-11=9
The answer is 1 remainder 9, or 1 + 9/11

If you divide by 0, you'll do this repeatedly forever. The amount of times that you'll need to subtract 0 will be infinity. So I guess you can say that there is an infinite amount of 0's in the number 4.
PatTheGreat42
0/0 can't be 1 because then you could prove any fraction is equal to any other fraction. For example, if 0/0 was 1, then if you take the equation 1/2 = 1/3, and then multiplied both sides by the same number, 1, expressed as 0/0, then your equation would become 0/0 = 0/0, which is true, except that it would show that 1/2 = 1/3, which obviousely isn't true. That make any sense?
sondosia
Yeah, anything divided by zero is "undefined", not infinity. Therefore 0/0 should be undefined too. My graphing calculator agrees with me on this one.

Interesting question though!
Aless
It is an imaginary number. If you actually had to divide zero by zero (impossible, obviously), the universe would split and we would all be swallowed by big black holes .
Arnie
So 0/0 is undefined. But what is
 Code: lim    (x/x) x-->0
mafiawars
zero divide zero equals zero there's nothing there to divide so why would it be infinity just abit of a daft question really but depends on who has the mathematical brain think I spelt that right I think.
raine dragon
It's a way to make a computer explode? ^^;
rvec
 raine dragon wrote: It's a way to make a computer explode? ^^;

Try what Afaceinthematrix said is a way to compute the answer of 4/0

 Code:

tell me when you get the answer

btw: please don't use this or anything like this on the frihost server
MarzEz
well, 0/0 can't be a way to make a computer explode. i'll prove it. start menu, all programs, accessories, calculator, 0/0...
why is the computer making that sound?
OH SHI-
Afaceinthematrix
 sondosia wrote: Yeah, anything divided by zero is "undefined", not infinity. Therefore 0/0 should be undefined too. My graphing calculator agrees with me on this one. :-) Interesting question though!

Again, it is undefined because when you divide anything by zero, the value is too infinitely great to be defined by numbers. It's not called infinity, and it would be improper to do so, but it is too infinitely large to be defined by numbers. 21/7 = 3 because there are three 7's in 21. There are an infinite amount of 0's in 21. That's why many mathematicians, and I, and many math books explain the concept of undefined simply meaning that the product would be too infinitely great to meaningfully define with numbers. This is the best way to explain it in a way that everyone, or at least most people, will understand.

 mafiawars wrote: zero divide zero equals zero there's nothing there to divide so why would it be infinity just abit of a daft question really :D but depends on who has the mathematical brain think I spelt that right I think.

No. It's undefined. You cannot divide by 0.

Arnie wrote:
So 0/0 is undefined. But what is
 Code: lim    (x/x) x-->0

That is one. That is in the indeterminate form. That reduces to 1, so the limit will simply be one. It's sort of like saying:

lim(x->0) 4
That's obviously 4. Now multiply the top and bottom by x.
You get lim(x->0) ((4x)/x).
This is the same equation (except at x=0 there will be a whole) so the limit will be the same. Many times when you take the limit and get 0/0, it actually has a limit but is in the indeterminate form. A perfect example is:
lim (x->0) sinx/x

That produces 0/0, but using the L'Hopital's (not sure on the spelling) Rule, that can be changed to:
lim (x->0) cosx/1 which will give you 1/1. Therefore the answer is 1. If it wasn't for that, technically you would be able to screw up any function by multiplying it by x/x.
MarzEz
well, is it undefined, (we'll call it infinity for now,) or is it 1?
you supplied 2 awnsers in your previous post.
i know undefined isn't the same as infinity, but there's no "undefined" in the poll.
Arnie
So, that answers the question. 0/0 is undefined, but when approached with a limit it's 1. Nothing more to say here, but I'm sure there will be plenty of heroes posting their random ideas without having read the rest of the topic anyway.
 Arnie wrote: So, that answers the question. 0/0 is undefined, but when approached with a limit it's 1. Nothing more to say here, but I'm sure there will be plenty of heroes posting their random ideas without having read the rest of the topic anyway.

it depends on the limit.
because with limits you can use x/x, 2x/x, x/2x,or in general nx/mx that will all go to 0/0 when x goes to 0. But the limit will be different. In general it will be n/m so if you choose n=1 and m=1 it is 1 but not with different values of n and m.
Davidgr1200
What does dividing nothing by nothing mean?
Dividing 1 by four, for example, means dividing 1 thing into four parts
Thus, dividing 0 by 0 means dividing nothing into no parts.
personally I think the question is meaningless
catscratches
 Davidgr1200 wrote: What does dividing nothing by nothing mean? Dividing 1 by four, for example, means dividing 1 thing into four parts Thus, dividing 0 by 0 means dividing nothing into no parts. personally I think the question is meaningless
Uses of division is not only to divide things into parts. It's usable in example programming too. Eg. what's -1 cookies divided into 4 parts? (-1/4).

0/0 is unusable though as it is undefined and can't be used in any way.

0/0 can be many things depending on what logic you use.

x/x = 1
3/3 = 1
2/2 = 1
1/1 = 1
0/0 = 1

x/0 = Infinity
3/0 = Infinity
2/0 = Infinity
1/0 = Infinity
0/0 = Infinity

And the logic meaning that division is dividing something into parts. With 0 you have nothing to divide and therefore the answer is 0.
Afaceinthematrix
 MarzEz wrote: well, is it undefined, (we'll call it infinity for now,) or is it 1? you supplied 2 awnsers in your previous post. i know undefined isn't the same as infinity, but there's no "undefined" in the poll.

It's undefined. In my previous post, I was simply answering someone's question about limits (one of the fundamental concepts in calculus and analysis). But 0/0 is undefined.
0 divided 0.. looks like an infinity ammount of debate on the answer to me
uuuuuu
For a somewhat authoritative answer to this question, I would refer anyone to this link:

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

Or this one:

http://en.wikipedia.org/wiki/L%27hospital%27s_rule

And here are my two cents:

People, maybe because it is comforting to their minds, like to believe that there is a Universal objective truth, and that it's comprehensible to man.

I personally believe in Universal truth, too. But I don't believe in my own capacity, having finite knowledge and time, to comprehend it.

The ironclad arguments of logic depend on at least a couple of things: The law of the excluded middle, which states more or less that for a proposition P, P is either true or false. In my many days, I have not come across a proposition in the truth of which EVERYONE was convinced.

Another block in this rickety tower is dependence on first principles or axioms which must be taken on faith. Any claim of truth based on logical rules must ultimately rely on believing in something "because I said so", or "because it's self evident", or by some other dependence on faith.

I believe that mathematical and logical truths derive their power from agreement on their truth. The more powerful argument is that which convinces more people.

And now, after all of that pussyfooting and wishy-washing around, here is a convincing argument of the indeterminacy of 0/0, grabbed straight from wikipedia:

 Quote: The most common example of an indeterminate form is 0/0. As x approaches 0, the ratios x2/x, x/x, and x/x3 go to 0, 1, and \scriptstyle\infty correspondingly. In each case, however, if the limits of the numerator and denominator are evaluated and plugged into the division operation, the resulting expression is 0/0. So (roughly speaking) 0/0 can be 0 or it can be \scriptstyle\infty and, in fact, it is possible to construct similar examples converging to any particular value. That is why the expression 0/0 is indeterminate. More formally, the fact that the functions f and g both approach 0 as x approaches some limit point c is not enough information to evaluate the limit \lim_{x \to c} \frac{f(x)}{g(x)}. \! That limit could converge to any number, or diverge to infinity, or might not exist, depending on what the functions f and g are. Not every undefined algebraic expression is an indeterminate form. For example, the expression 1/0 is undefined as a real number but is not indeterminate. This is because any limit that gives rise to this form will diverge to infinity. An expression representing an indeterminate form may sometimes be given a numerical value in settings other than the computation of limits. The expression 00 is defined as 1 when it represents an empty product. In the theory of power series, it is also often treated as 1 by convention, to make certain formulas more concise. (See the section "Zero to the zero power" in the article on exponentiation.) In the context of measure theory, it is necessary to take \scriptstyle 0\cdot\infty to be 0.

Love to all!

Uwe[/url]
draganuta
You cannot divide anything to 0 because its impossible. So the result i think its Chuck Norris
raine dragon
rvec wrote:
 raine dragon wrote: It's a way to make a computer explode? ^^;

Try what Afaceinthematrix said is a way to compute the answer of 4/0

 Code:

tell me when you get the answer

btw: please don't use this or anything like this on the frihost server

Yeah, I'm thinking not... Infinite while loop much? XD
J-Evil
rvec wrote:
 raine dragon wrote: It's a way to make a computer explode? ^^;

Try what Afaceinthematrix said is a way to compute the answer of 4/0

 Code:

tell me when you get the answer

btw: please don't use this or anything like this on the frihost server

I ran that on my computer lol. Used 100% system resources for 30 seconds then I got this:

 Quote: Fatal error: Maximum execution time of 30 seconds exceeded in C:\wamp\www\0divide.php on line 6

Anyways 0/0 is Chuck Norris OBVIOUSLY. His parents tried dividing by 0 one day and 9 months later Chuck was born!
Drawingguy
It has been already mentioned, but just to reaffirm, the talk about l'hopital's rule is right. 0/0 is undefined, but the limit of some fraction, where, as you approach a certain number, the quotient is that 0/0 thing, can have a defined answer. What l'hopital's rule is saying, in a simple way, is that if you have two functions that equal 0, as the input approaches some value (take the limit as x approaches pi, of sin(x)/(x-pi), for example), you can take the derivative of the top and bottom function, and that resultant quotient is equivalent to the previous fraction. In the case given, I think it would come out to be -1, since the derivative of sin(x) is cos(x), and the derivative of x-pi is simply 1, and cos(pi) divided by 1 is -1. Unless I'm thinking wrong, but I still think the concept is relatively right.
Afaceinthematrix
 Drawingguy wrote: In the case given, I think it would come out to be -1, since the derivative of sin(x) is cos(x), and the derivative of x-pi is simply 1, and cos(pi) divided by 1 is -1. Unless I'm thinking wrong, but I still think the concept is relatively right.

Your answer is correct. The answer is -1. However, your explanation is a little sketchy. You forgot the mention one of the most important points of the rule. One major point of L'Hospital's rule is to be able to compute the limit of a function that is in an indetermined form, but that still has a limit that isn't undefined. For instance, the limit as x approached 0 of 4x/x is 4. If you computed the limit the normal way, you would get 0/0. However, using L'Hospital's rule, you get 4/1 which is simply 4.
Psycho_X52
I was taught that maths forbids x/0. You can use it at limits only...

lim0/0= Another*Chuck^Norris-Beats*the*crap+of/everyone *1/sqrt(film)
x->Chuck Norris

Afaceinthematrix
 Psycho_X52 wrote: I was taught that maths forbids x/0. You can use it at limits only...

No, you can't. You cannot use it at limits. The L'Hospital's rule allows you to change those functions into something else so that you can use them.
indianinworld
0 is not a dividable figure. It almost doesnot exit. To quantify this in figures, they have 0 and it cannot be divided with 0 again.

Keep Smiling !!! - Keep Living

_________________
as alwayZz - Cheers and Cherish
indianinworld
Visit me @ : http://www.sathish.frih.net
indianinworld
As far as my knowledge goes 0 divided by 0 is infinity. But i could see people giving answers as 0.

NOW CONFUSED AND NOT SURE THOUGH !!!!!!!! ha ha haaaaaaaaaaa

Keep Smilng - Keep LiVIng....

_________________
as alwayZz - Cheers and Cherish
indianinworld
Visit me @ : http://www.sathish.frih.net
Arnie
Hmm, I take back my previous post. That l'Hospital's rule is quite interesting although I'm glad I don't have to use it in my chemistry maths course.
MarzEz
thanks heaps for all your ideas. I've managed to decide myself that the answer is 0 for 2 reasons:

if you have no people, and no pieces of cake, and you want to divide the cake evenly among he people, the universe doesn't spontaneously explode because it contains an infinite amount of cake.

let's take a classic example of reversal: 2x3=6, and 6/3=2. therefore if 0x0=0, then 0/0=0.

and there you have it. 0 divided by 0 is 0.
Afaceinthematrix
 MarzEz wrote: thanks heaps for all your ideas. I've managed to decide myself that the answer is 0 for 2 reasons: :arrow: if you have no people, and no pieces of cake, and you want to divide the cake evenly among he people, the universe doesn't spontaneously explode because it contains an infinite amount of cake. :arrow: let's take a classic example of reversal: 2x3=6, and 6/3=2. therefore if 0x0=0, then 0/0=0. and there you have it. 0 divided by 0 is 0.

No! I keep saying this. 0/0 is undefined. It is in no way, shape, or form 0! It's undefined! You cannot divide by 0! You can't just "decided yourself" because there is no opinion involved. It is just fact and basic math 101.
MarzEz
yes... it's undefined... which is why i've decided to define it, as 0.
the reason i defined it as 0 can be clearly seen in my previous post.
Afaceinthematrix
 MarzEz wrote: yes... it's undefined... which is why i've decided to define it, as 0. the reason i defined it as 0 can be clearly seen in my previous post.

Ok... you define it as 0. Have fun. In the mean time, I'm going to use your "definition" of 0/0 to prove to you that 0=1.

a = b + 1 Given
(a-b)a = (a-b)(b+1)
a^2 - ab = ab + a - b^2 - b
a^2 - ab -a = ab + a -a - b^2 - b
a(a - b - 1) = b(a - b - 1)
a = b
b + 1 = b
Therefore, 1 = 0

How can 1=0? That's completely incorrect! Well if you look at the line that I put in bold, you'll see that I divided both sides by a-b-1. If you look at the given line, you'll see that a = b + 1. Therefore, a - (b + 1) = 0. Using the distributive property, you'll see that a - b - 1 = 0. Therefore, when I divide both sides by a - b - 1, I'm really doing this:

a((a - b - 1)/(a - b - 1)) = b((a - b - 1)/(a - b - 1))
a(0/0) = b(0/0)

So if what you said was correct, I'd get:
0 = 0, which is correct. The math would be all good. But, since 0/0 does not equal 0, you get problems. You cannot divide by 0. When you try, things get all messed up.
MarzEz
that's because a(a - b - 1) is NOT equal to b(a - b - 1)
in the first one, you end up with A x A, A x B and A x 1. in the other one you get B x A, B x B, and B x 1. it's not the same.
Afaceinthematrix
 MarzEz wrote: that's because a(a - b - 1) is NOT equal to b(a - b - 1) in the first one, you end up with A x A, A x B and A x 1. in the other one you get B x A, B x B, and B x 1. it's not the same.

That's completely 100% incorrect. a(a - b - 1) IS equal to b(a - b - 1)... unless you're telling me that 0 doesn't equal 0? You seriously need to take a look at this website and learn some basic math. http://www.math.com/homeworkhelp/BasicMath.html

Edit:

Oh, and I just saw the second part of your post...
a^2 - ab -a = ab + a -a - b^2 - b

That is true. Both sides are equal. Everything in that proof is true up until you get a = b (which is the line after you divide both sides by zero.)
Arnie
 MarzEz wrote: let's take a classic example of reversal:
In Soviet Russia, zero divides YOU!
ankitdatashn
If we go by a simple logic then first comes 0 (of the numerator) then the / sign (which represents dividing) then after that comes 0 again which is the denominator. Now lets go step by step about it:-

First is 0 so let us think about 0, what is 0?, is it nothing??, hope so, then we cannot divide nothing by anything, so it means nil or 0.

now lets shift the number scale to left by 1, now the 0 become 1. now same we do to the denominator. then 1 divided by 1 will be 1 as any single thing that is taken as a whole is also single, so the answer is 1.

now same way shift the number scale for numerator to 50 points in left and denominator to 50 points in the right.so the numerator becomes 50 and denominator becomes -50. 50 divided by -50 yields -1.

Likewise I think 0 divided by 0 can give us the results of the whole answer scale, got it everyone??
hofodomo01
conventional math just kinda fails when a zero gets in the denominator. all of the workarounds that involve dividing by zero don't actually divide by zero either. they just use numbers...close to zero...
Afaceinthematrix
 ankitdatashn wrote: Likewise I think 0 divided by 0 can give us the results of the whole answer scale, got it everyone??

No, it cannot give us results. I keep saying this: you cannot divide by zero. It is undefined!
nivinjoy
I had not thought of that till now...???? Very confusing one...!! But in my opinion the answer is undefined....

I checked the same in Microsoft Calculator....The answer for 0/0 comes as "Result of function is undefined"....

So now what you guys say....?????????????? I have no comments....because i am not clear with the answer....!!!!
zjosie729
I believe 0/0 is undefined, and that should be one of the choices for the poll. Think about this: you can't divide 1 apple into 0 pieces. That's just not possible.
Arnie
Well, you can't divide an apple in 0.5 piece either but still 1/0.5 is defined. Besides, with 0/0 there's not 1 apple but 0.
Genesiz
It is infinity or undefined, whatever you want to call it. I think i can prove this using basic mathematics (i'm doing advanced maths and even i don't get some of the answers), but do correct me if i'm wrong:

If we make 0/0 = x, rearranging this becomes 0 = x0. Now x can be 1 (one zero equals zero), or 2 (two zeroes equals zero) or 3 (you get my point). If we carry this one, x becomes infinity (which i will replace with I). Substituting this into the original equation gives:

0 = I0, which can be rearranged to become 0/0 = I. I is infinity, and so 0/0 equals infinity.

Hopefully this will help to clear up any discrepancies, and i challenge anyone to prove me wrong.
catscratches
You proved yourself wrong.

0=1*0 is correct.
And so is 0=2*0.

just like you said.

It is not infinity. It is anything. There's an infinity OF ANSWERS!
Genesiz
Ok, so rather than infinity i will say it is undefined.

However from the list of answers infinity would be the best one to choose so....
jeremyp
In purely mathematical terms, the answer is "undefined".

Mathematically, division is defined in terms of multiplication

a/b is the number c such that a = b x c

If a is non zero and b is zero, clearly there is no answer. There is no number c such that a = 0 x c.

However, if a is zero there is an infinite set of answers. i.e. any number c satisfies 0 = 0 x c. The answer is therefore undefined, but in a different way to the way it is undefined if a is non zero.
MeddlingMonk
Mathematically, zero divided by zero is undefined (actually, anything divided by zero is technically undefined).

For example, take the graph of 1/(x+1). For the limit as x approaches negative 1, 1/(x+1) approaches infinity (1 divided by smaller and smaller increments gets closer and closer to infinity).

When x actually equals negative 1, though, 1/(x+1) is no longer any number that can be defined - there is no "increment" to divide by. Hence anything divided by zero is considered undefined.
uuuuuu
Here's my problem with this poll, though I've already chimed in with an answer above:

The authorities on this matter are ALL in agreement concerning the division of 0/0.

0/0 is an Indeterminate Form. That's all there is to it. It's not 0, it's not 1, it's not infinity, and it's not Chuck Norris. Chuck Norris is only one zero.

So, I refer all who do not understand the nature of an indeterminate form, again, to the wikipedia article:

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

for an AWESOME lesson in math.

But as to the subjectivity of this poll, there is VERY LITTLE.

An equally subjective poll might go something like:

What's 2+2?

a) 5
b) 3
c) 2
d) Rick Astley.

But now that I've spoken so ill of this poll, I WOULD like to compliment the questioner in asking a question that provokes thought, and educates people. You are awesome.

To the rest of you, say hi to your moms for me...

Until next time,

Love,

Uwe
It's not right to divide that. It just isn't.

Chuck Norris counted to infinty twice.
aames_prov356
You cannot divide anything by zero, so the answer is undefined.
blackheart
Think of it in primary school terminology: How many groups of nothing are there in nothing?

You can't have a group of nothing. Therefore the group does not exist. Undefined.

Or am I wrong?

=> Jess
Afaceinthematrix
 blackheart wrote: Think of it in primary school terminology: How many groups of nothing are there in nothing? You can't have a group of nothing. Therefore the group does not exist. Undefined. Or am I wrong? :P => Jess

You aren't wrong. You are 100% correct.
indianinworld
 Tubbz wrote: Chuck Noris invented God, so he is also the equivalence to 0 divided by 0.

Who invented god ??
ocalhoun
Haha!
Fake
Infinite.

biljap
0 divided by 0 is undefined because of this equation:
0/0 = x/1

X can equal any number and still satisfy that equation by the cross multiplication method.
missdixy
I like to think it's infinity.
ThornsOfSorrow
Actually, zero divided by zero is not undefined; it's indeterminate. When a math problem is undefined, that means that there is no answer. For example, when you divide 2 by 0, you're essentially trying to determine what multiplied by 0 gives you an answer of 2. There is no number that can do that. On the other hand, zero divided by zero gives you an infinate number of answers, so it's indeterminate.

Here's an example for those of you who understand limits and simple derivatives:
If you want to find the limit of 4x/x as x approaches zero, you will find that setting x equal to zero changes the equation to 0/0, thus giving an inteterminate answer. However, you can use L'Hopital's rule, taking the derivative of both sides to find the limit. Since the derivative of 4x is 4 and that of x is 1, the limit of 4x/x as x approaches zero is actually 4. Similarly, if the original equation was 5x/x or 2x^2/x, the same limit would be 5 or 0, respectively.

So zero divided by zero is indeterminate, not undefined.
Arnie
So according to you 0/0 is undetermined, but 2/0 is undefined. However, taking the derivative of 2/0 I get 0/0.
skygaia
simply... it's impossible to divide zero by zero. it's kind of definitions in math.
ThornsOfSorrow
 Arnie wrote: So according to you 0/0 is undetermined, but 2/0 is undefined. However, taking the derivative of 2/0 I get 0/0.

You're right, but I was only taking the derivative of those functions because I was using L'Hopital's rule which can only be used when the limit is 0/0 or infinity/infinity. It doesn't work for any other form. Because of that, the limit of 2/x as x approaches 0 would simply be undefined. You're not allowed to take the derivative in order to change that.
Afaceinthematrix
 ThornsOfSorrow wrote: Actually, zero divided by zero is not undefined; it's indeterminate.

sorta... you're technically correct but but for the purpose of this discussion, it's far easier to say undefined because if you're trying to explain to someone why you can't divide by zero, then they aren't going to understand the difference anyways. It's better to teach algebra before calculus.
FriBogdan
I'm going with undefined .

This is a classic case when you learn at school how to deal with limits . Most of the times you can find a solution but in this case you won't find any.
chartcentral
According to Microsoft XP's Calculator program, zero divided by zero: "Result of function is undefined."
ThornsOfSorrow
Afaceinthematrix wrote:
 ThornsOfSorrow wrote: Actually, zero divided by zero is not undefined; it's indeterminate.

sorta... you're technically correct but but for the purpose of this discussion, it's far easier to say undefined because if you're trying to explain to someone why you can't divide by zero, then they aren't going to understand the difference anyways. It's better to teach algebra before calculus.

I completely agree with you, but I just couldn't stay out of the conversation due to the fact that math has always been my favorite subject. However, seeing as I was taught that 0 divided by 0 is undefined until my college professors corrected me, I will hold my tongue from now on.
Afaceinthematrix
ThornsOfSorrow wrote:
Afaceinthematrix wrote:
 ThornsOfSorrow wrote: Actually, zero divided by zero is not undefined; it's indeterminate.

sorta... you're technically correct but but for the purpose of this discussion, it's far easier to say undefined because if you're trying to explain to someone why you can't divide by zero, then they aren't going to understand the difference anyways. It's better to teach algebra before calculus.

I completely agree with you, but I just couldn't stay out of the conversation due to the fact that math has always been my favorite subject. However, seeing as I was taught that 0 divided by 0 is undefined until my college professors corrected me, I will hold my tongue from now on.

i understand your desire to stay in the conversation and correct that. i'm working on my math major, so i often have the desire to come in a say something... i didn't learn the difference either until i was a senior in high school.
Arnie
There was a time that we were taught 5-6 isn't possible and there's no such thing as capital letters.
datter
ANY poll that has an option to answer "Chuck Norris" gets an instant seal of approval.
Afaceinthematrix
 Arnie wrote: There was a time that we were taught 5-6 isn't possible and there's no such thing as capital letters.

Really? I was never taught that. I was never taught that something impossible was possible (except in church).
ocalhoun
^He must be referring to some point in elementary school, teaching addition and subtraction before they explained the concept of negative numbers. Perhaps he expects to be taught some day that 0/0 is possible, just as he was taught one day that 5-6 is possible.

Perhaps the problem is that our concept of 0 is a little incomplete. 0 is a special case in so many operations...
j0yfuln0is3

It's actually impossible. There is no solution to the equation x ÷ 0, for that matter 0 ÷ 0
You're just trying to be difficult
catscratches
Yes, x / 0 often has a solution (unless it's 0). Infinity.
Arnie
 ocalhoun wrote: ^He must be referring to some point in elementary school, teaching addition and subtraction before they explained the concept of negative numbers. Perhaps he expects to be taught some day that 0/0 is possible, just as he was taught one day that 5-6 is possible.
I do not, you have to see my post in the context of the one above it and the quotes there - to which I replied.

Still, were you taught sqrt(-1) is impossible? I was. But then in university quantum mechanics kick in...
TiffanyTerrorXO
I would say Chuck Norris because...
well its him..
Soulfire
 Quote: infinity, because anyhting divided by 0 is infinity.

No, anything divided by 0 is undefined.

Ergo, 0/0 does not exist. It is undefined.
tony
Firstly, I like how chuck norris is winning the poll!!!!!!!!!!!!!1

Secondly, how is this for a maths problem?

-1 = -1
-1/1 = 1/-1
sqrt(-1/1) = sqrt(1/-1)
sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1)
sqrt(-1)*sqrt(-1) = sqrt(1)*sqrt(1)
-1 = 1
Cuncha
I make it 16.
mewmewlazlo
Well, first off if you have zero of "anything" you have nothing of "it". and two divide nothing of something by nothing means that you did no dividing at all because you had nothing to do anything with like divide in this case. But 1 also makes sense, even though it does not work.
Shazephre
rvec wrote:
 Gieter wrote: If you divide by 0, the universe will collapse. At least that's what they teached me in math classes.

Well at least php does
 Quote: Warning: Division by zero in /var/www/null.php on line 2

looooooooooool
dude..technically AND unanimously...its accepted as infinity

 MarzEz wrote: what is 0 divided by 0? does anyone know? well, technicaly it could be any of the following: 0, because 0 divided by anything is 0. infinity, because anyhting divided by 0 is infinity. 1, because anything divided by itself is 1. chuck norris, because he feels like it. http://www.chucknorrisfacts.com/ so, what's your opinion? i personally think it's chuck norris, but my second option is 1.
TerrorBite
Division by Zero: An Example

 ThornsOfSorrow wrote: Actually, zero divided by zero is not undefined; it's indeterminate. When a math problem is undefined, that means that there is no answer. ... On the other hand, zero divided by zero gives you an infinate number of answers, so it's indeterminate.

I agree with ThornsOfSorrow here. After reading the Wikipedia article on indeterminate form, and based on my own knowledge of mathematics, I can clearly understand that 0/0 is an indeterminate function. In layman's terms,
 catscratches wrote: It is not infinity. It is anything. There's an infinity OF ANSWERS!

So therefore, I can state that 0/0 = 42 and be correct (for some value of 0/0).
When it comes to nonzero divisions by zero however, I'm happy to think that x/0=∞, x≠0.

 linkmenot wrote: dude..technically AND unanimously...its accepted as infinity

Only in cases where the numerator is nonzero. See above.
infinity I say!
Josso
Nothing divided by nothing is surely nothing.

My 2 cents.
Nick2008
I don't know, it can be every answer.

So here goes, {All Real Numbers}
goutha
according to the pole it's = Chuck Norris.

Now I know!
Afaceinthematrix
 catscratches wrote: Yes, x / 0 often has a solution (unless it's 0). Infinity.

No. It will approach infinity. Infinity isn't a number.

 tony wrote: Firstly, I like how chuck norris is winning the poll!!!!!!!!!!!!!1 Secondly, how is this for a maths problem? -1 = -1 -1/1 = 1/-1 sqrt(-1/1) = sqrt(1/-1) sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1) sqrt(-1)*sqrt(-1) = sqrt(1)*sqrt(1) -1 = 1

The rules of square roots (as from line 3 to 4) do not work with negative numbers. They only work with real numbers.

No. Not really. You cannot just have infinity. Something will approach there. Besides, it's technically in the indeterminate form (which is something completely different). I sometimes will tell people it's undefined if they aren't ready to learn about the indeterminate form.
MarzEz
after reading these recent posts, i have come to the conclusion that 0/0=<pick a number, any number>.
and there is only one thing in this world that equals every single number at once.
as the poll would suggest, we are forced to accept that 0/0=Chuck Norris.
0/0 is not undefined. it can be defined.
watch me define it:
0/0=74.581
so is any other number, or string of letters.
however, the most conclusive answer is simply that 0/0=0/0
end of story.
Josso
I'm now hugely confused, a friend of mine pointed out to me that 0 fits into 0 once but that would be mathematically impossible?

Is there an actual article or research on this somewhere?
Afaceinthematrix
 Josso wrote: I'm now hugely confused, a friend of mine pointed out to me that 0 fits into 0 once but that would be mathematically impossible? Is there an actual article or research on this somewhere?

No. 0 Can fit into 0 an infinite amount of times. But that's beside the point. When teaching someone who's new to mathematics, I will always tell them that it's undefined because it's easier for them to understand. It's actually in the indeterminate form. For instance, if you think about the graph y=(5x)/x, you will see that there is a whole at x=0. That will produce 0/0. Now if you take the limit as x-->0, you will get 5. Get what I'm saying?
andredesignz
For other uses, see Division by zero (disambiguation).

In mathematics, a division is called a division by zero if the divisor is zero. Such a division can be formally expressed as where a is the dividend. Whether this expression can be assigned a well-defined value depends upon the mathematical setting. In ordinary (real number) arithmetic, the expression has no meaning.

In computer programming, integer division by zero may cause a program to terminate or, as in the case of floating point numbers, may result in a special not-a-number value (see below).

Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to is contained in Bishop Berkeley's criticism of infinitesimal calculus in The Analyst, see Ghosts of departed quantities.
Fatality
It's undefined, but if I had to pick one of the option it would be 0. Zero can't be divided by itself, thus you still have zero.
Josso
Afaceinthematrix wrote:
 Josso wrote: I'm now hugely confused, a friend of mine pointed out to me that 0 fits into 0 once but that would be mathematically impossible? Is there an actual article or research on this somewhere?

No. 0 Can fit into 0 an infinite amount of times. But that's beside the point. When teaching someone who's new to mathematics, I will always tell them that it's undefined because it's easier for them to understand. It's actually in the indeterminate form. For instance, if you think about the graph y=(5x)/x, you will see that there is a whole at x=0. That will produce 0/0. Now if you take the limit as x-->0, you will get 5. Get what I'm saying?

Hmm, I perhaps need more explanation. It's an interesting concept, is there a good article somewhere? Thanks for trying to explain btw.
Afaceinthematrix
Josso wrote:
Afaceinthematrix wrote:
 Josso wrote: I'm now hugely confused, a friend of mine pointed out to me that 0 fits into 0 once but that would be mathematically impossible? Is there an actual article or research on this somewhere?

No. 0 Can fit into 0 an infinite amount of times. But that's beside the point. When teaching someone who's new to mathematics, I will always tell them that it's undefined because it's easier for them to understand. It's actually in the indeterminate form. For instance, if you think about the graph y=(5x)/x, you will see that there is a whole at x=0. That will produce 0/0. Now if you take the limit as x-->0, you will get 5. Get what I'm saying?

Hmm, I perhaps need more explanation. It's an interesting concept, is there a good article somewhere? Thanks for trying to explain btw.

Try: http://en.wikipedia.org/wiki/Indeterminate_form

That gives a basic explanation of the concept. I'll take from some of their examples. If you take the limit as x-->0 of x/x, it would seem that you would get 0/0. Yet if you study the graph or work this out numerically, it will become clear that you will get 1 (as every value will be 1 and that can be reduced to 1). Another more tricky example that they give is the limit as x---->0 of (sinx)/x. If you plug 0 in for x (because a limit is assuming that a value, x, is becoming so close to 0, or whatever x approaches, that it pretty much becomes it) you will get 0/0. Yet if you study the graph, or check it numerically (plug in 0.1, 0.01, 0.001, 0.0001, etc. into the equation), you will see that the answer is one. That one is trickier. You need to use something called L'hospitals Rule to reduce that to (cosx)/1, which then in turn produce 1.
elyo-luk
If you have nothing, and you give it to nothing, how many of nothing get nothing ?

If you do this question to windows calc, you'll get undefined.

My "casio" calc says "Math Error"

My nokia phone says "Imposible dividir entre cero" (imposible to do 0/0)
Donutey
I think the real question, is does your question have any practical value?
Utopia GFR
This is what my Palm Pilot (Z22) says when I make the division :
-e-

I guess that means error.

On my laptop with Vista (French version), the advanced calculator displays "Résultat de fonction non défini" meaning function not defined error

It's nice to inject some fantasy or give irrational results in mathematics

Anyways, I answered Chuck Norris for I believe he is the mastermind of fat humor
Nothing divided by nothing is still nothing, but it can be infinity as well. Because if you put it into another context, you can divide forever. Which means, 0 dividing by 0 will be repeated forever, which means, infinity. But still 0 divided by 0 will be 0. And when you see zero like a 'thing', because it can be written down, you even can say the answer will be 1.

I say this is a trick question
First I thought it was the same as all the other values divided by zero. Infinity is not a value so I think say infinity is the answer would be wrong. but 0/a where a goes towards 0 is definitely 0.

On the other hand if we think that we have 0 apples that we should give to 0 persons. How many apples does each person get? This question does not make sense because there are no persons. The question must be wrong and therefore has no answer. Therefore I believe that 0/0 is not defined (if it must have a value it should have the value 0).
Afaceinthematrix
 Donutey wrote: I think the real question, is does your question have any practical value? :roll:

Yes it does. This is a very good and meaningful question with a lot of practicality. It is essential in understanding limits (and limits make up calculus and calculus is huge in science).

 Utopia GFR wrote: It's nice to inject some fantasy or give irrational results in mathematics :)

Sure it is. But 0/0 results in neither irrational numbers of fantasy.

 Lady Elensar wrote: Nothing divided by nothing is still nothing, but it can be infinity as well. Because if you put it into another context, you can divide forever. Which means, 0 dividing by 0 will be repeated forever, which means, infinity. But still 0 divided by 0 will be 0. And when you see zero like a 'thing', because it can be written down, you even can say the answer will be 1.

You can't just say that it is undefined because you do not actually know where the value will be. Read previous threads about the indeterminate form or do some research.
Afaceinthematrix
Sorry double post...
mwsupra
Lol, chuck norris is winning!

IMO zero divided by zero is just an invalid value, or NULL
Afaceinthematrix
 mwsupra wrote: Lol, chuck norris is winning! IMO zero divided by zero is just an invalid value, or NULL :P

It's sad that people prefer Chuck Norris over real math.

Anyways... it's not necessarily an invalid value. I keep repeating that it's in the indeterminate form (the value cannot be determined).
Mrs Lycos
Obviously chuck norris!!! Because hes a master LOL! XD
Nick2008
I did 0÷0 on a calculator and the answer was 'Error.'

So 0÷0 is Error.

But quite simply, it's probably Chuck Norris.
achowles
It can't be done. It has no practical application. You can't divide nothing. How could you do it? Into how many pieces could you divide absolutely nothing? None.

In a purely mathematical sense the answer is 0. Simply because, in the context of division, the two zeroes would have no effect on one another.
Afaceinthematrix
 achowles wrote: It can't be done. It has no practical application. You can't divide nothing. How could you do it? Into how many pieces could you divide absolutely nothing? None. In a purely mathematical sense the answer is 0. Simply because, in the context of division, the two zeroes would have no effect on one another.

Okay... take 4. 4 clearly equals 4. Now multiply that by x/x. You're not changing anything, right? x/x is just 1. You're just multiplying 4 and 1. Now you have 4x/x. If you graph that, you'd get a horrizontal line, right (since it's just 4). But at zero, you'd have 0/0. Shouldn't it be 4, since the whole graph should be constant at 4? That's why (as I keep saying almost every other post), that it's in the indeterminate form. How can the answer, as you said, be 0? That doesn't make sense.
PatTheGreat42
0 over 0 has to be zero, because if it was 1, then you could make any fraction equal any other fraction. 1/1 * 0/0 = 2/2 * 0/0 if 0/0 equaled 1.
Arnie
0 and 1 are not the only options. All you did was rule out that it is 1, but that doesn't mean it has to be 0.

By that logic, I can say you are 12 years old because you're not 50 years old. Makes sense?
achowles
 Afaceinthematrix wrote: How can the answer, as you said, be 0? That doesn't make sense.

The 0 that is to be divided remains 0 as dividing it by 0 cannot happen. Not just in a practical sense, but also a purely mathematical one. Therefore it remains 0 by default as nothing has occurred to change it.

Essentially, what you're doing is akin to trying to jam a cube through a round hole and wondering how, in theory, you could distort the dimensions of the cube enough to make this possible. You're not going to fool a cube into becoming a cylinder any more than you're going to turn 0 into a number that can be divided or divided by.
Afaceinthematrix
achowles wrote:
 Afaceinthematrix wrote: How can the answer, as you said, be 0? That doesn't make sense.

The 0 that is to be divided remains 0 as dividing it by 0 cannot happen. Not just in a practical sense, but also a purely mathematical one. Therefore it remains 0 by default as nothing has occurred to change it.

Essentially, what you're doing is akin to trying to jam a cube through a round hole and wondering how, in theory, you could distort the dimensions of the cube enough to make this possible. You're not going to fool a cube into becoming a cylinder any more than you're going to turn 0 into a number that can be divided or divided by.

No, that's not what I am doing. What I am doing is simply understanding limits and understanding calculus (which is basic math in the grand scheme of mathematics). 0/0 is not 0. There's no way in hell it's 0. It's in the indeterminate form.

One may be able to argue that the indeterminate form doesn't apply here and that the solution is undefined, but there is no way that you can rightfully argue that it's 0 - that's just incorrect.

Afaceinthematrix
 PatTheGreat42 wrote: 0 over 0 has to be zero, because if it was 1, then you could make any fraction equal any other fraction. 1/1 * 0/0 = 2/2 * 0/0 if 0/0 equaled 1.

If 0/0 did equal 1 (which it doesn't... it doesn't equal 0 either), then what you said would be correct. All 1/1*0/0 = 2/2 * 0/0 would be saying is that 1=1. Big deal. That would simply to 1*1=1*1. So I don't see your point.
Arty
Wow...Why is this topic so active? xD

0/0 - Hmmm, well 1/0 is undefined, because you can't divide one zero times, but is it possible to divide ZERO zero times?
Xanatos
 Arty wrote: Wow...Why is this topic so active? xD 0/0 - Hmmm, well 1/0 is undefined, because you can't divide one zero times, but is it possible to divide ZERO zero times?

No, No it isn't. Nothing can be divided by 0. Even 0. It's impossible. As many in this thread have attested to.
achowles
 Afaceinthematrix wrote: No, that's not what I am doing.

You're right. My analogy was a little off.

Trying to divide a number higher than zero by zero is akin to trying to push a theoretical cube through a round hole (all the while not making a dent on the reality of the matter).

Trying to divide zero by zero however is more akin to trying to force a tesseract through a round hole.

You can't do it. There's nothing to be done. You start off with zero. Nothing happens to zero. Zero remains zero.
Arnie
Why are you defining the default behaviour of an operator to return exactly what was put into it?
hamza1122
The last time i checked chuck norris was pretty good at maths so i belief the answer is chuck norris. But my other opinion would have to be either infinity or zero.
Insanity
Undefined.

You can't divide by zero.
I think I get the humor aspect of your joke, but if you want to improve on your answer, don't pick a question that people will feel happier getting correct over the true aspect of the joke.......... if that makes ANY sense to you.

0
-- = Undefined
0

snowynight
Scientifically I dont think it is correct to divide this way.
But I think 0/0 will be infinite.
Because the world comes from nothing and ends in nothing with nothings in between.......
So nothing is everyting....
Arnie
"Scientifically" is not the same as "mathematically".
guissmo
Based on Mathematics, it's undefined.
So I guess it's none of the above choices.

Good idea for a topic though.
mtsbuild
definitely infinite... or better maybe its just space.... if you have nothing, divide it by 0 you end up with 2 unknowns that are unquantifiable and un categorise als there is nothing to justify...

i think the actualy answer is 0 however 0 in itself is a confusions as 0 is a number that represents 'somthing' but when a 'somthing' = 0 then surely the 'something' becomes a confusion as it is no longer a something, so 0 should always be nothing.
Xanatos
 mtsbuild wrote: definitely infinite... or better maybe its just space.... if you have nothing, divide it by 0 you end up with 2 unknowns that are unquantifiable and un categorise als there is nothing to justify... i think the actualy answer is 0 however 0 in itself is a confusions as 0 is a number that represents 'somthing' but when a 'somthing' = 0 then surely the 'something' becomes a confusion as it is no longer a something, so 0 should always be nothing.

Its an indeterminate form. It dos not equal zero and it does not equal infinity. Please read the thread before posting here please.
infinisa
This is a really simple one to understand.

What does division mean?

a/b=c means a=b*c (that's a definition, just like a-b=c means a=b+c)

So, let's suppose 0/0 has some well-defined value, and call it c

Then 0/0=c means 0=0*c

Well, that's true for any real value of c.

As there is no single value of c that does the job, we conclude that 0/0 is undefined.

Using the same reasoning as above, let's suppose 1/0 has some well-defined value, and call it c.

Then 1/0=c means 1=0*c

Since 0*c=0 for any real value of c, we conclude that 1/0 is not defined as a real number.

Given that 1/x gets ever larger (without limit) as x approaches 0 (downward from 1), it's tempting to say the answer is infinity (which is not, of course, a real number). This is a dangerous conclusion, however, though, because if x approaches 0 through negative values (from -1 up to 0) 1/x becomes an ever larger negative number, so the limit in this case is -infinity (not at all the same thing!). Just look at the graph of y=1/x. So when we say 1/0 is infinity, this must be taken figuratively, and not as a precise mathematical statement.
Vova
It is not defined. As well as 1/0 and 10/0. People! You talk nonsense. We only can speak about lim (f (x)/g (x)) at x-> a, where f (x)-> 0 and g (x)-> 0 at x-> a, but it already other theme. Learn mathematics)
daefommicc
x/0 is not defined for x != 0
0/0 is an indeterminate form and can be answered using limits concept
just cancel d factor dat makes the expression 0/0:

like f(x)= [x2 - 2x]/[x2 - 3x]
lim x -> 0 of f(x) = [x-2]/[x-3] = 2/3
all you can do is retain d continuity of the graph...

as for the exact value is concerned, its an indeterminate form (others being inf/inf, 1^0 etc)
Kaseas
0/0 can be any number, hence it's undefined.
Xanatos
 Kaseas wrote: 0/0 can be any number, hence it's undefined.

no it can't be any number. It is an indeterminant form that has no value.
Afaceinthematrix
 Xanatos wrote: no it can't be any number. It is an indeterminant for that has no value.

Kinda... he was sort of correct. It can technically have any value for any situation that provides that value... so while he was sort of incorrect by saying that it can just have any value, saying that the value depends on the situation, and there are an infinite amount of situations, you can have any value... It's pretty much like how in some situations, infinity-infinity can approach 1...
Xanatos
Afaceinthematrix wrote:
 Xanatos wrote: no it can't be any number. It is an indeterminant for that has no value.

Kinda... he was sort of correct. It can technically have any value for any situation that provides that value... so while he was sort of incorrect by saying that it can just have any value, saying that the value depends on the situation, and there are an infinite amount of situations, you can have any value... It's pretty much like how in some situations, infinity-infinity can approach 1...

Don't even start with that infinity-infinity thing. That is a whole other issue all together. When you refer to it having whatever value the situation calls for I assume that you are refering to the limit of the function? In which case it may approach a certain value, but it does not actually hold that value. If you are refering to something else then please explain.
Afaceinthematrix
Xanatos wrote:
Afaceinthematrix wrote:
 Xanatos wrote: no it can't be any number. It is an indeterminant for that has no value.

Kinda... he was sort of correct. It can technically have any value for any situation that provides that value... so while he was sort of incorrect by saying that it can just have any value, saying that the value depends on the situation, and there are an infinite amount of situations, you can have any value... It's pretty much like how in some situations, infinity-infinity can approach 1...

Don't even start with that infinity-infinity thing. That is a whole other issue all together. When you refer to it having whatever value the situation calls for I assume that you are refering to the limit of the function? In which case it may approach a certain value, but it does not actually hold that value. If you are refering to something else then please explain.

No, I am simply referring to a limit while in the indeterminate form. I think that's what Kaseas was referring to (although I think Kaseas was just being lazy when saying his/her ideas) which is why I brought it up. It's also not all that different from inf-inf... both are indeterminate and I was merely using an example to show that you can conclude some sort of value
Xanatos
Afaceinthematrix wrote:
Xanatos wrote:
Afaceinthematrix wrote:
 Xanatos wrote: no it can't be any number. It is an indeterminant for that has no value.

Kinda... he was sort of correct. It can technically have any value for any situation that provides that value... so while he was sort of incorrect by saying that it can just have any value, saying that the value depends on the situation, and there are an infinite amount of situations, you can have any value... It's pretty much like how in some situations, infinity-infinity can approach 1...

Don't even start with that infinity-infinity thing. That is a whole other issue all together. When you refer to it having whatever value the situation calls for I assume that you are refering to the limit of the function? In which case it may approach a certain value, but it does not actually hold that value. If you are refering to something else then please explain.

No, I am simply referring to a limit while in the indeterminate form. I think that's what Kaseas was referring to (although I think Kaseas was just being lazy when saying his/her ideas) which is why I brought it up. It's also not all that different from inf-inf... both are indeterminate and I was merely using an example to show that you can conclude some sort of value

But this value is not really a "real" value it is just something that a limit approaches. It still does not exist and does not take on any value necessary.
Afaceinthematrix
^^Well of course not. But Kaseas said that 0/0 can be any number, and so I assumed that he/she meant limits (because I don't think anyone really thinks 0/0 is any number... 0/0=4=0/0=6 so 4=6?, that would just be stupid) so I just assumed that he/she meant limits and I pointed that out because I wasn't sure if you thought he/she meant limits or literally...
shkhanal
Though the question is lot confusing, I believe it is infinity.
Xanatos
 shkhanal wrote: Though the question is lot confusing, I believe it is infinity.

anarhistu
 shkhanal wrote: Though the question is lot confusing, I believe it is infinity.

If you consider "0/0 = infinity" you will have:

a^(infinity) = a^(0/0)
you can write the a^(0/0) as radinal powered 0 of a powered 0. this will be 1. But a^(infinity) is infinity. By this results that infinity=1 (False)

If you consider "0/0 = 0" you will have:

a^(0)=a^(0/0)

you can write the a^(0/0) as radical powered 0 of a powered 0. By this results that 1 = 1 (True)

A simple transformation of writing form changes the result or not. This proofs that 0/0 is equal to 0.

Which, by the way, is FALSE!!!!

ps: please forgive my stupid explanation, but I am not familiar with microsoft equations.

Same shit, old craps
Xanatos
 anarhistu wrote: If you consider "0/0 = 0" you will have: a^(0)=a^(0/0) you can write the a^(0/0) as radical powered 0 of a powered 0. By this results that 1 = 1 (True) A simple transformation of writing form changes the result or not. This proofs that 0/0 is equal to 0. Which, by the way, is FALSE!!!!

Then what was the point of posting this if your proof that 0/0=0 isn't true, which you acknowledge. Sure it appears to work at first glance but it is still wrong. Here is why...

You say that a^(0/0)=[a^0]^(1/0)=1, however...
a^(0/0) also=[a^(1/0)]^0=infinity^0 which is another indeterminate form.

In general X^(a/b)=c if and only if (x^a)^(1/b)=c and [x^(1/b)]^a=c
anarhistu
Xanatos wrote:
 anarhistu wrote: If you consider "0/0 = 0" you will have: a^(0)=a^(0/0) you can write the a^(0/0) as radical powered 0 of a powered 0. By this results that 1 = 1 (True) A simple transformation of writing form changes the result or not. This proofs that 0/0 is equal to 0. Which, by the way, is FALSE!!!!

Then what was the point of posting this if your proof that 0/0=0 isn't true, which you acknowledge. Sure it appears to work at first glance but it is still wrong. Here is why...

You say that a^(0/0)=[a^0]^(1/0)=1, however...
a^(0/0) also=[a^(1/0)]^0=infinity^0 which is another indeterminate form.

In general X^(a/b)=c if and only if (x^a)^(1/b)=c and [x^(1/b)]^a=c

Thank you very much for your analyze, Xanatos. I do not think I need to say that your explanation is ok, because we all know that, but ... if you follow my explanation (stupid one, I admit again), please point what you think is wrong in it, cause I do not see. By my opinion, mathematically, is correct. So, transforming the square into a radical, we have a contradiction. That's what I wanted to point out: In my opinion, "0/0" is just illogical expression. Chuck Norris may be the answer, if he can drink beer and breath in the same time.

I do not agree what you guys said about the universe swallowed by a black hole (or something like that) if somebody can say he can divide something by 0. The universe is based on 0's no? The Hawking Radiation Theory is based on this. There is well known that from nothing appear two particles with equal but opposite masses and energies. Then they tend to re-become 0. I will not stay to discuss here the hawking radiation, but... please!!! Math is not only based on calculations! Math is not simply equations, but is also logical stuff.

Plus, I like that there are many who scream out loud that they are sure they are correct and all the others are wrong. I think, first of all, we should try to understand what we are discussing about and then start pointing the finger and destroy ideas and theories. I will also have something to discuss related to another post, but I will quote it directly.

All the best to you!
Xanatos
^^ you gave an explanation which stated that 0/0 was 0. you then stated that it was false without stating why. That is what I found wrong with your post.
anarhistu
 Xanatos wrote: ^^ you gave an explanation which stated that 0/0 was 0. you then stated that it was false without stating why. That is what I found wrong with your post.

I see what you meant. I said it is wrong related to this fact.. that regarding to 0/0 we can never say for sure that it is 0, infinit, or something else. At least this is what I think and what I was thinking about. Apologies for incomplete sentence in my initial post, but I was at work and please understand my hurry to finish posting. I promise next time I will explain more clear what I mean. Regarding the fact that I said is FALSE, consider that the explanation is also true, also false. That's what I wanted to pint out:

1) True part. Mathematically, my explanation is ok

2) False part. Also mathematically, we cannot have a radical ordered 0. It is like you would say that we have 1 kilogram of light. It is a fact that photons have mass, but we cannot weight the light in kilograms. Theoretically is correct, but logically is not. And please do not say that logic has nothing to do here. Somehow is the same with the error that proves 1=2

This is what I meant by false statement. Depends how you judge the analyze and depends on the conditions that need to be kept as a must.

Xanatos
^^ Mathematically your explanation was not okay because you failed to explain why 0/0 is not zero. That is all I was pointing out.
anarhistu
Now I did explained. It is ok now?
anarhistu
Xanatos wrote:
 anarhistu wrote: If you consider "0/0 = 0" you will have: a^(0)=a^(0/0) you can write the a^(0/0) as radical powered 0 of a powered 0. By this results that 1 = 1 (True) A simple transformation of writing form changes the result or not. This proofs that 0/0 is equal to 0. Which, by the way, is FALSE!!!!

Then what was the point of posting this if your proof that 0/0=0 isn't true, which you acknowledge. Sure it appears to work at first glance but it is still wrong. Here is why...

You say that a^(0/0)=[a^0]^(1/0)=1, however...
a^(0/0) also=[a^(1/0)]^0=infinity^0 which is another indeterminate form.

In general X^(a/b)=c if and only if (x^a)^(1/b)=c and [x^(1/b)]^a=c

Ok! But if you have x^0/0 and you transform it keeping the situation as power, you will have

x^0^(1/0). In this case you note 0=a and (1/0)=b. The situation becomes x^a^b. You have 3 ways of solving:

a) (x^0)^(1/0), that shall be 1^infinity, that shall have the result 1

b) (x^(1/0))^0, that shall be infinity^0, that shall have the result 1

c) x^(0^(1/0)), that shall be x^0, that shall have the result 1

Thinking again over those analyzes, I am sure that 0/0, even if seams to be an ilogical statement, has the result 0.

Infinity is not something else than a number, but a very big number, one that we just cannot imagine. In this situation, we can presume that infinity is equal to 10^10^10^10^10^10^10^10^....
Any existing number, natural, real, irational, any number powered 0 times shall be 1. same the infinity powered 0 times is also 1. Keeping the fact that infinity is a number, 0 powered an infinity times shall be zero. As simple example, we know that 0x0=0. That is equivalent to 0^2. Then 0^10 will be the same as 0^10000000000000 and the same with 0^A where A is any kind of number, from -infinity to plus infinity. The result will always be 1.
anarhistu
 badai wrote: actually, 0 / 0 can be both 1 and infinity. i cannot remember the exact thing, and even if i remember, i don't think i can explain it here. it was when i learned about lim (x -> 0) (f(x)/g(x)) that we discuss when x approaches 0, f(x)/g(x) can both be 1 or infinity. but then again, i need to ask chuck norris if he'll agree with it.

Actually, this is the mistake done when you have to calculate some specific thing.
Using the formula gaved by you here, the lim (x->0) (f(x)/g(x)), we are calculating a limit when x -> 0, but by this condition we get that x not equal to 0. It is eighter bigger, eighter smaller. But what we are trying to solve here is the exact 0. So, by my point of view, this has nothing to do with the request of the problem.
anarhistu
Afaceinthematrix wrote:
 vineeth wrote: Well, to answer this question, we must think a bit philosophical also. First lets define ZERO and the process of DIVISION

This isn't a philosophical question at all. It's a simply arithmetic problem at an elementary level. 0/0 = undefined.

My question here is: Are you really possitive that the unswer is undefined? Why?
pho3nixsky
Can't you just have no solution like in some quadratic equations there are no solutions.
Xanatos
 anarhistu wrote: Ok! But if you have x^0/0 and you transform it keeping the situation as power, you will have x^0^(1/0). In this case you note 0=a and (1/0)=b. The situation becomes x^a^b. You have 3 ways of solving: a) (x^0)^(1/0), that shall be 1^infinity, that shall have the result 1 b) (x^(1/0))^0, that shall be infinity^0, that shall have the result 1 c) x^(0^(1/0)), that shall be x^0, that shall have the result 1 Thinking again over those analyzes, I am sure that 0/0, even if seams to be an ilogical statement, has the result 0. Infinity is not something else than a number, but a very big number, one that we just cannot imagine. In this situation, we can presume that infinity is equal to 10^10^10^10^10^10^10^10^.... Any existing number, natural, real, irational, any number powered 0 times shall be 1. same the infinity powered 0 times is also 1. Keeping the fact that infinity is a number, 0 powered an infinity times shall be zero. As simple example, we know that 0x0=0. That is equivalent to 0^2. Then 0^10 will be the same as 0^10000000000000 and the same with 0^A where A is any kind of number, from -infinity to plus infinity. The result will always be 1.

I do not understand what you are getting at here. x^(1/0) is not the same as x^0^(1/0). I already showed you why using this approach does not prove that 0/0=0. What are you trying to prove?
anarhistu
Xanatos wrote:
 anarhistu wrote: Ok! But if you have x^0/0 and you transform it keeping the situation as power, you will have x^0^(1/0). In this case you note 0=a and (1/0)=b. The situation becomes x^a^b. You have 3 ways of solving: a) (x^0)^(1/0), that shall be 1^infinity, that shall have the result 1 b) (x^(1/0))^0, that shall be infinity^0, that shall have the result 1 c) x^(0^(1/0)), that shall be x^0, that shall have the result 1 Thinking again over those analyzes, I am sure that 0/0, even if seams to be an ilogical statement, has the result 0. Infinity is not something else than a number, but a very big number, one that we just cannot imagine. In this situation, we can presume that infinity is equal to 10^10^10^10^10^10^10^10^.... Any existing number, natural, real, irational, any number powered 0 times shall be 1. same the infinity powered 0 times is also 1. Keeping the fact that infinity is a number, 0 powered an infinity times shall be zero. As simple example, we know that 0x0=0. That is equivalent to 0^2. Then 0^10 will be the same as 0^10000000000000 and the same with 0^A where A is any kind of number, from -infinity to plus infinity. The result will always be 1.

I do not understand what you are getting at here. x^(1/0) is not the same as x^0^(1/0). I already showed you why using this approach does not prove that 0/0=0. What are you trying to prove?

Hi Xanatos,

Nobody said anything about "x^(1/0). It really is not the same with x^0^(1/0). But if you read the entire statement, it was "(x^(1/0))^0", which is something totally different than x^(1/0). I said that the calculation of the 0/0 power of x can be done in 3 different ways and I just said that your statement that "infinity^0 is another indeterminate form." is illogical by my point of view and I tried to explain shortly why.

What exactly is not clear in my expressions? Please do not get me wrong, but unless my explanation is incomplete, try to read the all argument before considering it wrong. Thanks!
anarhistu
 daefommicc wrote: x/0 is not defined for x != 0 0/0 is an indeterminate form and can be answered using limits concept just cancel d factor dat makes the expression 0/0: like f(x)= [x2 - 2x]/[x2 - 3x] lim x -> 0 of f(x) = [x-2]/[x-3] = 2/3 all you can do is retain d continuity of the graph... as for the exact value is concerned, its an indeterminate form (others being inf/inf, 1^0 etc)

Excuse me, but I have something unclear here:

if you started from
f(x) = [x2-2x]/[x2-3x]

and you therefore got the
lim(x->0) of f(x) = [x-2]/[x-3] = 2/3 ....

How did you got this answer?!!!? Id you started from [x2-2x]/[x2-3x]... and you know x->0 .... isn't it logic to replace all the "x" variables with 0? I mean .... from [x2-2x] you lost the second "x" and transformed the "2x" into "2". Same thing you did with the "3x" that became "3" ...
Or you just considered the conditions [x->0; x<=1; x>0] and by chance you used the upper limit for the second and the fourth variable and the lower limit for the other two variables? Or maybe you mistype the two "x"?
Please, explain to me cause I am a bit confused.. Maybe I did not understood the post....
Afaceinthematrix
 anarhistu wrote: Ok! But if you have x^0/0 and you transform it keeping the situation as power, you will have x^0^(1/0). In this case you note 0=a and (1/0)=b. The situation becomes x^a^b. You have 3 ways of solving: a) (x^0)^(1/0), that shall be 1^infinity, that shall have the result 1 b) (x^(1/0))^0, that shall be infinity^0, that shall have the result 1 c) x^(0^(1/0)), that shall be x^0, that shall have the result 1 Thinking again over those analyzes, I am sure that 0/0, even if seams to be an ilogical statement, has the result 0. Infinity is not something else than a number, but a very big number, one that we just cannot imagine. In this situation, we can presume that infinity is equal to 10^10^10^10^10^10^10^10^.... Any existing number, natural, real, irational, any number powered 0 times shall be 1. same the infinity powered 0 times is also 1. Keeping the fact that infinity is a number, 0 powered an infinity times shall be zero. As simple example, we know that 0x0=0. That is equivalent to 0^2. Then 0^10 will be the same as 0^10000000000000 and the same with 0^A where A is any kind of number, from -infinity to plus infinity. The result will always be 1.

You are very wrong on multiple levels.

I would go by line by line and analyze your original post, but it would be meaningless because you are making the same mistake over and over again. Infinity is not a number. It is a direction. Something approaches infinity. You cannot treat infinity as an integer because it is not. For instance, if we tried to treat infinity as a number, we could do a whole bunch of interesting things. 4*infinity will still equal infinity. So divide both sides by infinity and you'll get 1 = 1/4. That's obviously wrong. You cannot just raise something to the 1/0 power. It is meaningless. 1/0 will approach infinity. It does not equal infinity because NOTHING equals infinity. It will approach infinity. 1/0 is meaningless (undefined). You were also wrong when you said that infinity^0 is 1. It is not 1 because again, you cannot treat infinity as an integer. Infinity/infinity, infinity-infinity, infinity+infinity, 0/0, 0^0, infinity^0, and 0*infinity are all what we call indeterminate forms. You must do a little more work to figure out what their value will be; their value can equal an infinite amount of things.

Now going back to what you're currently saying:

anarhistu wrote:
 daefommicc wrote: x/0 is not defined for x != 0 0/0 is an indeterminate form and can be answered using limits concept just cancel d factor dat makes the expression 0/0: like f(x)= [x2 - 2x]/[x2 - 3x] lim x -> 0 of f(x) = [x-2]/[x-3] = 2/3 all you can do is retain d continuity of the graph... as for the exact value is concerned, its an indeterminate form (others being inf/inf, 1^0 etc)

Excuse me, but I have something unclear here:

if you started from
f(x) = [x2-2x]/[x2-3x]

and you therefore got the
lim(x->0) of f(x) = [x-2]/[x-3] = 2/3 ....

How did you got this answer?!!!? Id you started from [x2-2x]/[x2-3x]... and you know x->0 .... isn't it logic to replace all the "x" variables with 0? I mean .... from [x2-2x] you lost the second "x" and transformed the "2x" into "2". Same thing you did with the "3x" that became "3" ...
Or you just considered the conditions [x->0; x<=1; x>0] and by chance you used the upper limit for the second and the fourth variable and the lower limit for the other two variables? Or maybe you mistype the two "x"?
Please, explain to me cause I am a bit confused.. Maybe I did not understood the post....

That's a little bit of arithmetic, buddy. The limit as x --> 0 of (x^2 - 2x)/(x^2 - 3x) is clearly 2/3. If you just plug in 0 for x, you'll get 0/0. I already told you that 0/0 is an indeterminate, so we must do a bit of extra work to figure it out. Do some basic algebra and we'll get (x(x - 2))/(x(x - 3)), we cancel out a pair of x's, and we plug in 0. Yay! We got 2/3...
victornumber
0 divided by0 is undefined. None of your choices at th top of the poll show this so I'm going to say none of the above. Chuck Norris?!!!!!!!!!!!!!!!!!!!!!!!!! Did anyone actually put this on the poll!!!!!!!!. I'll go check it out.
Chris65536
Division by 0 is undefined because it returns all numbers at once, but also doesn't. An odd way to demonstrate this is graphically.

Consider a graph of 0 gradient (that's a horizontal line of the form f(x) = 0x + k). Pick a value of x, and you'll get a value for f(x) (which will be k). Try it if you don't believe me.

Now do k/0. This amounts to a vertical line. Now pick a point on x. For most points, you'll get nothing there: the value is undefined. For x = k, you'll get every value at the same time (since all values for f(x) map to the same x): it's still undefined, but it's undefined in a different way.

And for 0/0, k = 0. The problem is still undefined. Not infinity, not 0, just undefined.

(EDIT: almost had to revoke my maths license there. Slight error in the equation of a straight line. Fixed it now.

Incidentally, the maths may be a bit dodgy for k/0 for the inverse. I'm almost certain that's wrong, but you get the gist. I said I'd graphically show it!)
Afaceinthematrix
anarhistu wrote:
Afaceinthematrix wrote:
 vineeth wrote: Well, to answer this question, we must think a bit philosophical also. First lets define ZERO and the process of DIVISION

This isn't a philosophical question at all. It's a simply arithmetic problem at an elementary level. 0/0 = undefined.

My question here is: Are you really possitive that the unswer is undefined? Why?

For educational reasons, yes. In reality, no. People here don't seem to understand that 0/0 is not undefined, but in the indeterminate form (even though a couple people here have explained it zillions of times). People just don't get it because it seems like every time I come here to post, someone is talking about it being undefined (like the person who just posted above me) so I'll just go with if because until you get to calculus or any upper division math course it doesn't really matter... In basic algebra, it's really the same thing...
Xanatos
Can someone lock this thread please, this is getting to be absolutely ridiculous.

0/0 is indeterminant as has been explained many times. You don't need to post that it is undefined or zero or whatever else you think it is. This thread is done. It's becoming an artificial post increase rather than a discussion.
Afaceinthematrix
^^ I agree that it is getting annoying. Even though both of us have said at least a dozen times that it's indeterminate, people still keep calling it undefined. So I just decided to let them think that (to save my sanity, and because these people obviously haven't taken upper division math courses and if they do, they'll learn it anyways...)
Bikerman
Thread locked. I consider the explanations provided already as sufficient to the original question,
Bikerman