Forum Moderators: Robert Charlton & goodroi
I tried to divide by zero on the built-in calculator on my Apple Macintosh computer running OS 10.3.8.
"INFINITY"!
Bigger than life! Right there!
Apple Computer's opinion, anyway.
Ha. I love it. Great fun.
Zero divided by zero, however, yields
"Not A Number".
My sci-calc returns "illegal operation", and in mathematical language, that sums it up for me. Stop dummy! Move on, you're trying to do something that can't be done.
I'd rather play with Infinite Sets [mathforum.org].
"someNumber / 0" meaning : "Not divide this!" or "someNumber / false" or "someNumber / nothing"
and "someNumber / 0 = undefined" is'nt correct answer:
which undefined * 0 = my original someNumber?
I thing correct result is: someNumber / 0 is textual "ERROR, invalid request: You have tried to starting a process and same time you forbid to execute."
If you take the limit 1/x from above as x goes to 0 then that is infinity.
If you take the limit 1/x from below as x goes to 0 then that is negative infinity.
The limit of 1/x as x goes to 0 is undefined.
Getting back to Google they should give the answer "Undefined" or "Not A Number"
What about 0/0, which Google says is 0.
You could make the case the all numbers are valid answers,
so 0/0=0 and 0/0 = 20 (as 20*0=0). I know my math teachers would say that's wrong, but I don't see why.
Any Number / 0 = Google. ;)
To most mathematicians (except for those specialized in applied numerics), "calculating results" is an exceptionally boring proposal. Math isn't about calculating stuff. Math is about defining concepts and the relations between them. Ultimately, it's about describing the world.
And in this mathematical world, infinity is a very useful concept, and 1/0 is a perfectly valid relation describing equivalence to that concept.
Maybe looking at reciprocal values makes it easier to understand: Just as 5 (resp 5/1) is defined as reciprocal to 1/5, infinity is defined as reciprocal to zero:
x/0 == x*infinity == infinity
x*0 == x/infinity == 0What about 0/0, which Google says is 0
As shown, this is the same as 0*infinity, hence the result is indeed 0.
12/3 is 3+3+3+3 (so the answer is 4 as there are 4 number threes).
To divide by zero:
1/0 is 0+0+0+0+0+0+0+0+0+.... (you will never get it to add up to 1 by constantly adding zero)
So counting the zeros would be, well, forever. A maths name for forever is infinity. Infinity is not a number.
Infinity = Infinity + 1
Infinity/Infinity does not necessarily equal 1.
Infinity IS an undefined number, but is large in magnitude.
On some conference in like 1960
the BIGGEST NUMBER which exist in our UNIVERSE
was assigned to 10^100 ( 1 and 100 zeros after ).
And it was called GOOGLE.
So in our case 1/0 is infinity which closest match is
a GOOGLE!
I guess that's a little wordy for the Google, so my suggestion would be:
1/0 is undetermined.Search for divide by zero [google.com] to learn more about this mathematical problem.
The same trickery is used in those short series of equations that prove 1 equals 2.
You will usually find division by zero somewhere in the algebra.
The calcultors should return UNDEF or whatever to indicate undefined. -Larry
Any calculus professor will insist that n/0 is underfined.
I doubt that. It would be entirely reasonable to DEFINE infinity as n/0 where n is any positive value greater than zero.
Infinity is NOT indeterminate.
Infinity/infinity is indeterminate.
0/0 is indeterminate.
Infinity * 0 is indeterminate.
Infinity is a valid mathematical value just like pi. Pi cannot be written to absolute precision, but it does exist. Infinity cannot be written with absolute precision, but it does exist.
Kaled.
PS
It is often valid to say, for instance,
Infinity * Infinity * 0 = infinity
Infinity/infinity is indeterminate.
0/0 is indeterminate.
Surely they both = 1 ;)
1/1 = 1 , 2/2 = 1 ..... 1000000000/1000000000 = 1 ..... infinity/infinity
Likewise
0.5/0.5 = 1 , 0.2/0.2=1 ..... 0.0000000001/0.0000000001 = 1 ..... 0/0
Then
Infinity * Infinity = infinity/0
which is ofthen valid as well :)
Zero times infinity is still zero.
Zero times infinity is still zeroSometimes yes, sometimes no.
Consider, for example, a little 3D geomoetry.
Lets look at the surface z = y / x2
Lets look at the intersection with the plane x = y
so z = x / x2
so z = 1 / x
when x = 0, z = infinity
when x = infinity, z = 0
or, more accurately,
as x approaches zero, z approaches infinity
as x approaches infinity, z approaches zero.
When comparing infinite values, it is necessary to look at the speed at which infinity is approached with respect to other variables. For instance 1/x2 is always larger than 1/x (0 <= x < 1) even when x = 0.
Kaled.
I think if x=infinity then z cannot equal zero as it will always be a fraction. If we multiply both sides by x we get z times x must equal 1, and a zero for either the values z or x cancels the chance of that.
If I have 1 piece of pie and divide it among 0 pie eaters I still have 1 piece of pie!
mmmmmmmm good pie.
If I have 1 piece of pie and divide it among 0 pie eaters I still have 1 piece of pie
You haven't divided it.
If anyone thinks I'm talking nonsense, get some graph paper and a calculator. After an hour or so you will see that, in practical terms, I am correct. If you come to another conclusion it is because you are either stupid or some sort of mathematical purist who doesn't ever apply maths to the real world. (For instance, you can argue that +infinity = -infinity, but such arguments have no practical application.)
Vast quantities of modern technology are based on Fourier analysis. Calculating the area under curves is essential to this. This can only be done by taking a pragmatic approach to infinity. Since these technological devices do actually work, I think we can say that the pragmatic approach is correct - proven empirically.
Kaled.
The most common confusion is between the mathematical definitions, and the practical methods to calculate certain results. Those are two very different animals, each of which serves an entirely different purpose.
>>If I have 1 piece of pie and divide it among 0 pie eaters I still have 1 piece of pie
You haven't divided it.
Actually, he did.
And since zero people are eating, this one piece of pie is going to last forever. It's infinite.
Ain't mathematical purism fun? ;)
Instead of using infinity = 1/0 , if we multiply both sides by 0 we get infinity times 0 = 1 which is odd since anything times 0 = 0.
Perhaps that is why Google considers 1/0 = 0 and not infinity. Of coarse there isn't a number you can multiply by 0 to get one so even 0 is a bad answer. The only solution seems to be you can't divide by zero but only multiply by it.
I looked up "divide by zero" and got a couple of pages that confirm this.
So I think the answer is 1/0 = undefined
Logically the answer approaches infinity, but mathematically it can't be justified and is undefined.
So I think the answer is 1/0 = undefined
Depending on your definition of undefined, this is absolute nonsense.
1/0 = infinity
2/0 = infinity
n/0 = infinity where n is a positive value greater than 0
0 * infinity = undefined or indeterminate
"undefined" in this context, means has no meaningful value. Infinity is a perfectly valid value for a maths function.
Take the function y = 1/x2
The area under the curve in the range 1 < x < infinity is FINITE.
It's over twenty years since I studied maths, but I think I am solid ground when I say that this is an accepted mathematical fact.
Kaled.
Actually it makes perfect sense, you can't divide a number by zero. Here is a simple explanation-
Let's look at some examples of dividing other numbers.
10/2 = 5
This means that if you had ten blocks, you could
separate them into five groups of two.
9/3 = 3
This means that if you had nine blocks, you could
separate them into three groups of three.
5/1 = 5
Five blocks could be separated into five groups
of one.
5/0 =?
Into how many groups of zero could you separate
five blocks?
It doesn't matter how many groups of zero you have, because they would never add up to five since 0+0+0+0+0+0 = 0. You could even have one million groups of zero blocks, and they would still add up to zero. So, it doesn't make sense to divide by zero since there is not a good answer.
If you know a little bit about multiplication, you could look at it this way:
10/2 = 5 This means that 5 x 2 = 10
9/3 = 3 This means that 3 x 3 = 9
5/1 = 5 This means that 5 x 1 = 5
5/0 =? This would mean that the answer x 0 = 5, but
anything times 0 is always zero.
So there isn't an answer.
All your arguments and illogic concern integers. Well, here's some news for you - not all number are integers, not all numbers can be precisely represented. e and pi cannot be represented as fractions. No matter how many decimal places you calculate to, the pattern of digits never repeats. Nevertheless, these numbers do exist. pi is defined as the ratio of the circumference of a circle to its diameter. However, you cannot accurately represent it. Infinity cannot be represented but it is a valid value. Representing it as zero is certainly wrong. Representing it as undefined or indeterminate is also wrong unless you also subscribe to the argument that +infinity = -infinity. This may be true, but it is not useful.
In South America (I think) a nutcase dictator defined pi as 3.0
It would appear that there are more such nutcases in this world than I could ever have imagined.
Kaled.
What feeble argument are you talking about, the one that proves you can't divide by zero?
That argument isn't feeble, it is a fact.
If you use simple math you will see that, just turn the problem into multiplication instead of division and there is no way to multiply with zero to get one. e and pi have no part in this discussion, infinity does and you haven't shown how infinity times zero equals one because it doesn't, it equals zero. Nothing can be multiplied to get one, so the answer to what is 1/0 is it is undefined.
