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# Google caculator 1 / 0 = 0?!

## 1 / 0 = undefined. a Bug

#### coolma

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

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joined:Apr 11, 2005
posts:20

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.!

#### Brett_Tabke

1:41 pm on Apr 19, 2005 (gmt 0)

joined:Sept 21, 1999
posts:38255

lol - nice catch!

#### bloke in a box

2:37 pm on Apr 19, 2005 (gmt 0)

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posts:141

It's mathematically impossible to divide by zero.

Try dividing by zero in Windows Calculator or Excel etc, you'll get the same error. :)

#### Lord Majestic

3:06 pm on Apr 19, 2005 (gmt 0)

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posts:1679

It's mathematically impossible to divide by zero.

I beg to differ -- mathematically pretty much everything is possible: I believe 1/0 should be positive infinity -- its just computers and their non-mathematically inclined users will have difficulty grasping how big is the infinity ;)

#### arubicus

3:45 pm on Apr 19, 2005 (gmt 0)

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posts:570

Agree with LORD. It is not impossible just indeterminate.

Can infinity actually be an answer?

No it is an abstract concept (not a real number) so in this case cannot be used as an answer either. Dividing by zero is undefined but does in no way mean that it infinate.

#### Absolut

8:22 pm on Apr 19, 2005 (gmt 0)

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posts:3

Infinity is a concept, as is 1/0.

The closer the divisor gets to reaching zero, the closer the result comes to reaching infinity.

This is pure mathematics, people seem to be making the mistake that this are real integers.

#### bird

9:37 pm on Apr 19, 2005 (gmt 0)

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posts:1551

Well, 0 is as good an approximation to infinity as any other number... ;)

#### hdpt00

10:01 pm on Apr 19, 2005 (gmt 0)

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posts:737

0 is a pretty bad guess of infinity, in my engineering perspective.

#### Lord Majestic

10:05 pm on Apr 19, 2005 (gmt 0)

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posts:1679

Well, 0 is as good an approximation to infinity as any other number... wink

No it is not: 0, 1 or even googol are all much much smaller than (positive) infinity.

#### mole

11:10 pm on Apr 19, 2005 (gmt 0)

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posts:160

So 1/0 should be several googles?

#### Lord Majestic

11:15 pm on Apr 19, 2005 (gmt 0)

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So 1/0 should be several googles?

Lets just say that the infinity (which is the correct answer to 1/0 problem) is bigger than googol and google taken together ;)

#### arubicus

12:24 am on Apr 20, 2005 (gmt 0)

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posts:570

"Lets just say that the infinity (which is the correct answer to 1/0 problem)"

It isn't the correct answer. If 1/0 = infinity then what is 2/0. Twice infinity? Also if this is the case then you are saying that infinity x 0 = 1?

So any real number divided by zero = infinity(not a real number) then:

1/0 = infinity
2/0 = infinity

By this definition 1/1 should equal 2/1

[edited by: arubicus at 12:29 am (utc) on April 20, 2005]

#### theBear

12:28 am on Apr 20, 2005 (gmt 0)

#### Senior Member

joined:Mar 19, 2003
posts:804

Here you go:

Replace the two * with tt.

[mathforum.org...]

[edited by: ciml at 9:12 am (utc) on April 22, 2005]

#### Lord Majestic

12:30 am on Apr 20, 2005 (gmt 0)

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posts:1679

It is the correct answer to 1/0 problem, and it also happens to be the correct answer to 2/0 problem ;)

By this definition 1/1 should equal 2/1

Nope: 1/1 is not equal 2/1, where as 1/0 is equal (has same result) as 2/0. :)

Also if this is the case then you are saying that infinity x 0 = 1?

Now this is a good question that I can't remember exact answer to, but we can always google it ;)

#### arubicus

12:49 am on Apr 20, 2005 (gmt 0)

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"Nope: 1/1 is not equal 2/1, where as 1/0 is equal (has same result) as 2/0. :)"

The result would be nonsense because of 1/1 would have to = 2/1 if 1/0 has the same result as 2/0 if infinity were used as an answer to 2/0 = (notice the equal sign) and 1/0 both. Infinity cannot be a direct defined answer to both unless infinity itself is defined first.

Then I ask you how much is 2/0? Would it be twice infinity? Is that possible? Or is it the same? If it is the same then again 1/1 should also be equal to 2/1.

If infinity x 0 = 0 then where do you get 1 or 2 uless you substitute a REAL number! Hence again you are not defining what REAL number infinity is.

Also you are breaking the rule for all real numbers (I noticed you can find it on the website above also) a(b/a) = b. If a = 2 and b = 4 then 2(4/2) = 4

With the stated rule...

a = 0 and b = 1

0(1/0) should equal 1 not infinity.

#### Lord Majestic

1:04 am on Apr 20, 2005 (gmt 0)

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posts:1679

Also you are breaking the rule for all real numbers

Infinity is an abstract concept and its a cool answer to 1/0 problem :)

Hey, don't take it with me, take it with Abstract Algebra , you might want to search for "Limits and division by zero" on Google, plenty of interesting stuff :)

#### arubicus

1:55 am on Apr 20, 2005 (gmt 0)

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I am not saying infinity cannot be used in algebra in things such a limits (where you are defining a bit more) just not in this instance.

Take a pie and divide it zero ways. When you are done have you accomplished anything?

#### Lord Majestic

1:57 am on Apr 20, 2005 (gmt 0)

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posts:1679

Take a pie and divide it zero ways

Can't say about zero ways, but when my sister used to divide it 2 ways, I always gotten zero - explain that! ;)

#### arubicus

2:13 am on Apr 20, 2005 (gmt 0)

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LOL!

Sounds like my wife!

A woman thig is the only explaination.

#### Lord Majestic

2:26 am on Apr 20, 2005 (gmt 0)

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posts:1679

A woman thig is the only explaination.

You said it -- you just gotto believe it regardless of whether it is supported by any rational material explanation. ;)

#### TheRookie

2:28 am on Apr 20, 2005 (gmt 0)

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joined:Mar 12, 2005
posts:178

Hey, don't take it with me, take it with Abstract Algebra , you might want to search for "Limits and division by zero" on Google, plenty of interesting stuff

But the limit of 1/0 isn't the same as the answer of 1/0.

#### Lord Majestic

2:34 am on Apr 20, 2005 (gmt 0)

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posts:1679

But the limit of 1/0 isn't the same as the answer of 1/0

Its a cool, google-like, better answer that will make whoever seen it deep into magical world of abstraction that helped created computers as we know it. Is it not worth returning infinity as the answer rather than stupid "undefined"?

#### TheRookie

2:36 am on Apr 20, 2005 (gmt 0)

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joined:Mar 12, 2005
posts:178

Its a cool, google-like, better answer that will make whoever seen it deep into magical world of abstraction that helped created computers as we know it. Is it not worth returning infinity as the answer rather than stupid "undefined"?

Well, it isn't worth making it infinity it for a student using Google's calculator to answer math problems which may be graded! :-/

But having it = 0 doesn't help, either.

#### arubicus

2:37 am on Apr 20, 2005 (gmt 0)

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posts:570

I don't know I like the sound of indeterminate better:)

#### Lord Majestic

2:43 am on Apr 20, 2005 (gmt 0)

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posts:1679

Well, it isn't worth making it infinity it for a student using Google's calculator to answer math problems which may be graded! :-/

Hey, if you use Google (instead of knowing result straight away) to determine what is the result of 1/0 then you deserve the grade you will get ;)

Anyhow, its all very academical and this thread might just loop into infinity, so to wrap it up I personally favour the infinity as the right answer to the question, but I appreciate that most people would prefer to see something else.

#### arubicus

2:55 am on Apr 20, 2005 (gmt 0)

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are we going to infinity or 0 nowhere or is this convo undefined in direction? LOL OK I am done.

Peace everyone!

#### Lord Majestic

3:02 am on Apr 20, 2005 (gmt 0)

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posts:1679

Peace everyone!

Yeah, tell your wife that my sister says hi -- they are clearly from the same race or something ;)

#### arubicus

3:11 am on Apr 20, 2005 (gmt 0)

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joined:Aug 27, 2003
posts:570

Bunch of pie eating aliens!

#### woop01

3:32 am on Apr 20, 2005 (gmt 0)

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joined:Feb 25, 2003
posts:972

ICK

Reading some of the results from that Google search brought up "L'Hopital's Rule". I have honestly had a horror movie like response to just seeing that term.

#### bird

2:18 pm on Apr 20, 2005 (gmt 0)

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joined:Aug 10, 2001
posts:1551

> Well, 0 is as good an approximation to infinity as any other number... wink

No it is not: 0, 1 or even googol are all much much smaller than (positive) infinity.

Since all those number are an infinite distance away from infinity, each of them is equally suited as an approximation. That doesn't mean they're good approximations, just that there are no better ones... ;)

It isn't the correct answer. If 1/0 = infinity then what is 2/0. Twice infinity?

Yes. Just that infinity multiplied by any non-zero number is again infinity.

Also if this is the case then you are saying that infinity x 0 = 1?

No. Any number (including infinity) multiplied by zero results in zero:
infinity * 0 = 0

You need to look at zero and infinity as opposed concepts, and it will eventually start to make sense. At both ends of the scale there are a few special cases to deal with.

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