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Google caculator 1 / 0 = 0?!
1 / 0 = undefined. a Bug
coolma




msg:744415
 3:37 pm on Apr 15, 2005 (gmt 0)

I love google. so i test all the functions out that provided by google.
But one day my friend asked me what is 1 / 0? I know it but i can not remember how to say it,the teminology. What I was sure is it is undefined or should be error(computer science students always treat it as a runtime error)
and then I searched on Google , its caculator function which is the same place as keyword input textfield, just type 1 / 0. and search it will give you the result. I was supprised that Google got me 1 / 0 = 0, as a science student, I am sure it is wrong. So I e-mail google team to let them know this arithmetic bug. (was excited) After a couple of days I got mail from them with "Thanks" , pretty good aye. But until now it is still not fixed.
I asked my friend who is good at math about the name of this "error".
Then I know It is undefined. anything / 0 = undefined.!

 

arubicus




msg:744445
 5:10 pm on Apr 20, 2005 (gmt 0)

I think we closed this yesterday:)

Sally Stitts




msg:744446
 7:05 pm on Apr 20, 2005 (gmt 0)

One more data point, just for fun.

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".

digitalghost




msg:744447
 7:40 pm on Apr 20, 2005 (gmt 0)

My Win XP calc returns, "cannot divide by zero". I much prefer that over "infinity" as there is no "answer" and infinity isn't quite correct. The equation is asking how many zeros can go into 1 and there is no answer to that exact question, and no, I don't think "infinity" is a proper answer.

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].

composer




msg:744448
 5:46 am on Apr 21, 2005 (gmt 0)

"someNumber / 0" is'nt real division.

"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."

racer_x




msg:744449
 7:28 am on Apr 21, 2005 (gmt 0)

1/0 is undefined. To claim it is infinity is just wrong.

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"

arubicus




msg:744450
 7:32 am on Apr 21, 2005 (gmt 0)

And racer wins the gold!

Robert Thivierge




msg:744451
 8:16 am on Apr 21, 2005 (gmt 0)

For 1/0, I'm in the "undefined" camp (Racer said it best).

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.

shri




msg:744452
 8:19 am on Apr 21, 2005 (gmt 0)

If someone has a sense of humor...

Any Number / 0 = Google. ;)

bird




msg:744453
 10:47 am on Apr 21, 2005 (gmt 0)

Jut because my pocket calculater can't dig 1/0, doesn't mean there's no definition for it.

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 == 0

Whether knowing that is of any use to you and me is of course an entirely different story... ;)

What about 0/0, which Google says is 0

As shown, this is the same as 0*infinity, hence the result is indeed 0.

PCInk




msg:744454
 10:57 am on Apr 21, 2005 (gmt 0)

To divide by a number, you are stating how many times this number goes into the first, eg:

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.

photo200




msg:744455
 6:53 pm on Apr 21, 2005 (gmt 0)

To be serious.

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!

ciml




msg:744456
 11:40 am on Apr 22, 2005 (gmt 0)

When dividing the number one by successively smaller numbers, the solution tends towards positive or negative infinity. Although this is useful in some algebraic contexts, one should always be aware that 1/0 is undetermined.

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.


mrMister




msg:744457
 2:12 pm on Apr 22, 2005 (gmt 0)

And it was called GOOGLE

Err, I think you mean googol [google.co.uk]

TerrCan123




msg:744458
 5:07 am on Apr 26, 2005 (gmt 0)

1/0 isn't 0, it approaches infinity as the denominator approaches zero like many of you said. They need to add another answer to this as an explanation, perhaps they are Googling it to see what to do?

TerrCan123




msg:744459
 5:10 am on Apr 26, 2005 (gmt 0)

I wish my net worth was 1/0.

larryhatch




msg:744460
 5:42 am on Apr 26, 2005 (gmt 0)

Any calculus professor will insist that n/0 is underfined,
for any real number n. There is good reason for this.
Using otherwise valid algebraic operations, you can make n/0 equal anything!

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

kaled




msg:744461
 9:05 am on Apr 26, 2005 (gmt 0)

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

gpmgroup




msg:744462
 9:41 am on Apr 26, 2005 (gmt 0)

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

varbano




msg:744463
 9:54 am on Apr 26, 2005 (gmt 0)

===========
PS
It is often valid to say, for instance,
Infinity * Infinity * 0 = infinity
===========

Then

Infinity * Infinity = infinity/0

which is ofthen valid as well :)

bird




msg:744464
 11:37 am on Apr 26, 2005 (gmt 0)

It is often valid to say, for instance,
Infinity * Infinity * 0 = infinity

Zero times infinity is still zero.

kaled




msg:744465
 1:59 pm on Apr 26, 2005 (gmt 0)

Zero times infinity is still zero
Sometimes 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.

TerrCan123




msg:744466
 6:50 pm on Apr 26, 2005 (gmt 0)

so z = 1 / x
when x = 0, z = infinity
when x = infinity, z = 0

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.

irritated




msg:744467
 7:05 pm on Apr 26, 2005 (gmt 0)

If I have 6 pieces of pie and divide it among 2 pie eaters they each will get 3 pieces of pie.

If I have 1 piece of pie and divide it among 0 pie eaters I still have 1 piece of pie!

mmmmmmmm good pie.

kaled




msg:744468
 10:43 pm on Apr 26, 2005 (gmt 0)

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.

bird




msg:744469
 12:12 am on Apr 27, 2005 (gmt 0)

Numbers are awfully abstract concepts, even if most people don't really notice, because we use (some of) them all the time.

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? ;)

TerrCan123




msg:744470
 6:13 am on Apr 27, 2005 (gmt 0)

The problem still exists on the conversion to a multiplication instead of a division.

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.

kaled




msg:744471
 9:08 am on Apr 27, 2005 (gmt 0)

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.

TerrCan123




msg:744472
 6:22 pm on Apr 27, 2005 (gmt 0)

Depending on your definition of undefined, this is absolute nonsense.

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.

kaled




msg:744473
 10:45 pm on Apr 27, 2005 (gmt 0)

By this feeble argument, e and pi do not exist.

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.

TerrCan123




msg:744474
 5:34 pm on Apr 28, 2005 (gmt 0)

By this feeble argument, e and pi do not exist.

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.

kaled




msg:744475
 6:14 pm on Apr 28, 2005 (gmt 0)

So, all the great mathematicians of the world and of recent history are all wrong. Infinity does not exist as a mathematical concept, instead we must use the term "undefined"....... nonsense.

As I said earlier, a reasonable definition is
infinity = n/0 where n is any value greater than zero. In other words, n is undefined except for being greater than zero.
So, rearranging the equation, infinity * 0 = n. So infinity * 0 is undefined (but positive). This is also what I said earlier.

I don't recall having ever defined infinity as being equal to 1/0.

I can't remember much of it but I do have a subsidiary degree in Maths. I've studied Fourier theory, Nyquist theory, numerical analysis and stuff that I can't even remember the names of. All these require a reasonable definition of infinity. But I guess you know better than everyone else.

Kaled.

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