# Division by Zero

• Just wanted to let everyone know its now ok to divide by zero.

•  Oh, cool, thanks.

• Meth shipment finally got through that blockade NYC set up, huh?

•  Just wanted to let everyone know its now ok to create nonsensical threads on whatever ill-conceived thought stumbles out of your brain.

• 0/0 = 0

5/0 = 8

8/0 = 13

13/0 = 21

log(log(x)) ≈ 5

Almost all natural numbers are very, very, very large.

• @Welbog said:

0/0 = 0

5/0 = 8

8/0 = 13

13/0 = 21

log(log(x)) ≈ 5

Almost all natural numbers are very, very, very large.

Cool, it's the Da Vinci fibonacci sequence!!! Is this some kind of code to the holy grail?  Are you in the priory?

• I'm Spider-Man.

• @Welbog said:

I'm Spider-Man.

That's only half true!

•  I prefer my zeros to be made of granite.  Less likely to get stolen that way you know.

•  It has always been okay.

> 1/0

Uncaught Exception: Divide by zero

We're so paranoid about null pointer exceptions these days... at least be nice to our friend, the divide by zero exception.

• Forgetting computers for the moment, back in elementary school math, I could never understand why you couldn't divide by zero.  It seems to me anything divided by zero would just simply be ... zero.  After all, that's just as logical as x/1 = x.  Saying that dividing by zero was undefined and impossible never seemed logical to me.

It was one of those irritating math rules that I never comprehended but just went along with to avoid arguments.

So I'm glad now to hear the silly rule has been lifted, thanks!

• @jetcitywoman said:

It was one of those irritating math rules that I never comprehended but just went along with to avoid arguments.
I always understood that it's because you can't prove it.  You say that 1/0 is zero.  Ok, how do you prove it?  by multiplying zero by zero to get ... zero?  aha!  it's not 1!

I say that 1/0 is -17.  -17 * 0 = 0, not 1.  Looks like I'm wrong too.

Some people consider it to be infinity, because the Lim(1/x) as x approaches 0 gets really high and in theory would be infinity when it hits zero.  I can't argue with that, and I like it better than saying it's undefined.

• @belgariontheking said:

@jetcitywoman said:

It was one of those irritating math rules that I never comprehended but just went along with to avoid arguments.
I always understood that it's because you can't prove it.  You say that 1/0 is zero.  Ok, how do you prove it?  by multiplying zero by zero to get ... zero?  aha!  it's not 1!

I say that 1/0 is -17.  -17 * 0 = 0, not 1.  Looks like I'm wrong too.

Some people consider it to be infinity, because the Lim(1/x) as x approaches 0 gets really high and in theory would be infinity when it hits zero.  I can't argue with that, and I like it better than saying it's undefined.

You're wandering dangerously close to hallowed ground.  These are the lands of the math nerd, and should you cross them, you will be sorry.  Please, walk away while your kneecaps still work.

• @jetcitywoman said:

It was one of those irritating math rules that I never comprehended but just went along with to avoid arguments.
I suspect you might be trying to make me rage out, but just in case you're actually serious here's an explanation:

Division is defined to be multiplication by multiplicative inverse. What that means in layman's terms is when you say z=x/y, you're actually saying z=x*w where w is the number with the property y*w=1 (w is y's inverse or w=1/y). You can't divide by 0 because there is no number w such that 0*w=1. Division by zero is undefined, therefore, because 0 has no inverse.

You can try to come up with various "patches" to multiplication to allow for an inverse of 0, but as soon as you do that, the system you're defining can no longer be something called a ring, which you can think of as basic arithmetic. If your operations don't make a ring, a lot of simple mathematical common sense no longer applies. Rings necessarily don't allow for an inverse of the additive identity, which is usually 0.

• @belgariontheking said:

Some people consider it to be infinity, because the Lim(1/x) as x approaches 0 gets really high and in theory would be infinity when it hits zero.  I can't argue with that, and I like it better than saying it's undefined.
Well the limit of (x-1)/(sqrt(x)-1) as x approaches 1 is 2. That doesn't mean 0/0 is 2. You can't prove things by example.

• @Welbog said:

You can try to come up with various "patches" to multiplication to allow for an inverse of 0, but as soon as you do that, the system you're defining can no longer be something called a ring, which you can think of as basic arithmetic. If your operations don't make a ring, a lot of simple mathematical common sense no longer applies. Rings necessarily don't allow for an inverse of the additive identity, which is usually 0.
Technically, you're discussing a field, not a ring.  Division need not work in a ring.

• @Welbog said:

I suspect you might be trying to make me rage out, but just in case you're actually serious here's an explanation:

As I posted, I thought it would have probably been more beneficial to my education if a teacher walked us through a proof instead of just issuing mandates, so I'm really glad you posted this.

@Welbog said:

z=x/y, you're actually saying z=x*w where w is the number with the property y*w=1 (w is y's inverse or w=1/y). You can't divide by 0 because there is no number w such that 0*w=1

So let me work this through on a couple examples.

z=x/y       ==   z=x*w (where y*w=1)

z=4/0    ==  z=4*w (where 0*w=1)   yep, doesn't work.

z=4/1   ==  z=4*w  (where 1*w=1)  means w=1 so this pans out

z=4/3   ==  z=4*w   (where 3*w=1)  hmmm....  have I mentioned that I hate math?   What's the value of w in this example to make this work?

• @bstorer said:

@Welbog said:
You can try to come up with various "patches" to multiplication to allow for an inverse of 0, but as soon as you do that, the system you're defining can no longer be something called a ring, which you can think of as basic arithmetic. If your operations don't make a ring, a lot of simple mathematical common sense no longer applies. Rings necessarily don't allow for an inverse of the additive identity, which is usually 0.
Technically, you're discussing a field, not a ring.  Division need not work in a ring.
I knew someone would say that, but I didn't bother describing why because I figured anyone who knows what a field is can do this in his head without me holding his hand:

A ring's additive inverse has the property that 0+x=x for all x, including x=0. Therefore 0=0+0. Therefore x*0 = x*(0+0) = x*0 + x*0 => x*0 - x*0 = x*0 + x*0 - x*0 => x*0 = 0 for all x. Therefore even in a ring the property that there is no x such that 0*x=1 is true.

• @jetcitywoman said:

z=4/3   ==  z=4w   (where 3w=1)  hmmm....  have I mentioned that I hate math?   What's the value of w in this example to make this work?
One third

•  let's forget about all the weird talk of 1/0=infinity... infinity isn't a number.

Statements like "lim (x -> 0) of f(x) = Infinity" doesn't mean infinity is a number; if you take a look at the definition of such a statement, it's somewhere along the lines of "f(x) can be taken arbitrarily large with a value of x sufficiently close to 0". It's NOT defined as "the difference between f(x) and infinity ..."

• Ah, I had a feeling it was 1/3, but... maybe I'm tired today. Cool, that makes sense.

• @Welbog said:

@bstorer said:

@Welbog said:
You can try to come up with various "patches" to multiplication to allow for an inverse of 0, but as soon as you do that, the system you're defining can no longer be something called a ring, which you can think of as basic arithmetic. If your operations don't make a ring, a lot of simple mathematical common sense no longer applies. Rings necessarily don't allow for an inverse of the additive identity, which is usually 0.
Technically, you're discussing a field, not a ring.  Division need not work in a ring.
I knew someone would say that, but I didn't bother describing why because I figured anyone who knows what a field is can do this in his head without me holding his hand:

A ring's additive inverse identity has the property that 0+x=x for all x, including x=0. Therefore 0=0+0. Therefore x*0 = x*(0+0) = x*0 + x*0 => x*0 - x*0 = x*0 + x*0 - x*0 => x*0 = 0 for all x. Therefore even in a ring the property that there is no x such that 0*x=1 is true.

FTFY

• @bstorer said:

FTFY

• I always figured that if i gave 5 items to zero people, i simply can not know how many items each person gets because there are no people. Or more simply put, the "action" can not be preformed. Which at least to me makes sense.

I fully know math isn't based on giving people items or multiplying items, but i guess i just fail at using numbers without a physical foot hold. This gives me much trouble with imaginary numbers though. ( not sure if that's also called as such in english, but it's SQRT(-1) )

Strangely enough i have no problem understanding most  2d/3d algorithms though, but i guess i can just more easily apply those to (virtual) physical objects.

• @stratos said:

I always figured that if i gave 5 items to zero people, i simply can not know how many items each person gets because there are no people. Or more simply put, the "action" can not be preformed. Which at least to me makes sense.

I fully know math isn't based on giving people items or multiplying items, but i guess i just fail at using numbers without a physical foot hold. This gives me much trouble with imaginary numbers though. ( not sure if that's also called as such in english, but it's SQRT(-1) )

Strangely enough i have no problem understanding most  2d/3d algorithms though, but i guess i can just more easily apply those to (virtual) physical objects.

That's how I was taught about division by zero by my mom when I was 5.  She said five candies dividied by zero kids cannot possibly be done.

• @morbiuswilters said:

@stratos said:

I always figured that if i gave 5 items to zero people, i simply can not know how many items each person gets because there are no people. Or more simply put, the "action" can not be preformed. Which at least to me makes sense.

I fully know math isn't based on giving people items or multiplying items, but i guess i just fail at using numbers without a physical foot hold. This gives me much trouble with imaginary numbers though. ( not sure if that's also called as such in english, but it's SQRT(-1) )

Strangely enough i have no problem understanding most  2d/3d algorithms though, but i guess i can just more easily apply those to (virtual) physical objects.

That's how I was taught about division by zero by my mom when I was 5.  She said five candies dividied by zero kids cannot possibly be done.

I particularly like how the left-land-side remains of young Johnny, when cleanly severed in twain, is nevertheless fortunate enough to then get 10 candies.

• Wow, everyone's been talking about how while x/0 is undefined for all x not equal to zero, but nobody has mentioned that 0/0 is in fact not undefined but simply indeterminate, since 0*x = 0 for all x.

My favorite response to "what is 0/0?" is "anything you want!"

Of course, I hate it when trying to solve singular systems and the result is a useless (though true) expression like "x = x" or "1 = 1".  Makes me wonder where in three pages of scribbling I have gone wrong....

Wow, everyone's been talking about how while x/0 is undefined for all x not equal to zero, but nobody has mentioned that 0/0 is in fact not undefined but simply indeterminate, since 0*x = 0 for all x.
Everyone already knows that 0/0 is nullity.

• @Welbog said:

Everyone already knows that 0/0 is nullity.

There I was thinking it was FILE_NOT_FOUND.

Good thread, I'm going to make my six year old read it to make sure he ends up better at maths, sorry math, than me.

Unless you start swearing.

• import paulaBean;

function divide(x, y) {

if(y == 0) {

if(x == 1) return infinity;

if(x == 0) return FILE_NOT_FOUND;

print(paulaBean.getPaula());

return 0;

} else return x/y;

}

• @belgariontheking said:

the Lim(1/x) as x approaches 0 gets really high and in theory would be infinity when it hits zero.

You have misunderstood the idea of limits.

A.  you can't say "in theory" when dealing with concrete math like this.  It is all "in fact"

2. In fact it would be undefined with it hits zero, not infinity.

D. Just as something to think about, you were talking about x approaching 0 from the positive side.  If x were approaching 0 from the negative side then the limit would be approaching negative infinity.

So in conclusion:

While "some people [might] consider [1/0] to be infinity," those people have no clue what they are talking about.

•  Or you could've just simply said, infinity is not a number, nor FILENOTFOUND.

•  Limits are interesting and this conversation is making me remember calculus. The idea of approaching the limit always made my head feel funny - xenos paradox.

Anyway, a cool application of limits with respect to topology (I think) is discussed in this documentary about knot theory called "not knot" - worth a look if you have some time.

Not Knot (Part 1/2) – 08:01
— britoca

• @chebrock said:

Limits are interesting and this conversation is making me remember calculus.

L'Hôpital? That's the first that popped up my mind when relating "0/0", Limits and basic Calculus.

The reasoning for x/0 being "Infinity" stems from the idea of the divisor approaching zero; the division result would go higher and higher. Of course, if the divisor's negative, then it approaches negative infinity. (Or, as some people joke, knocked down 8.) The best way to see this is doing something like

y = 1/x

which is known as an asintote, because of its behavior when the divisor component approaches zero.

• @danixdefcon5 said:

which is known as an asintote asymptote, because of its behavior when the divisor component approaches zero.

• @bstorer said:

@danixdefcon5 said:

which is known as an asintote asymptote, because of its behavior when the divisor component approaches zero.

Damn. Should've asked the Babelfish before posting.

• @tster said:

@belgariontheking said:

the Lim(1/x) as x approaches 0 gets really high and in theory would be infinity when it hits zero.

You have misunderstood the idea of limits.

A.  you can't say "in theory" when dealing with concrete math like this.  It is all "in fact"

2. In fact it would be undefined with it hits zero, not infinity.

D. Just as something to think about, you were talking about x approaching 0 from the positive side.  If x were approaching 0 from the negative side then the limit would be approaching negative infinity.

So in conclusion:

While "some people [might] consider [1/0] to be infinity," those people have no clue what they are talking about.

In fact, there are different theories in mathematics, and in some of them the function 1/x maps 0 to infinity - or, so to speak 1/0 = infinity. Those theories do not involve fields, as shown above, and so you still can't divide by zero.

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