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How to Divide by Zero

Last posted Jun 10, 2011 at 09:47PM EDT. Added Jun 09, 2011 at 11:16AM EDT
27 conversations with 18 participants

Ok, so you know how everyone tried to do it? I finally succeeded.

It hit me in Calculus class about a week ago.
So, in calc, where reciprocals are concerned, as x approaches 0, y approaches infinity? But it’s also true that as x approaches infinity, y approaches 0.

Graph:

In that case, anything divided by infinity will be 0. Take out a calculator and witness this effect: Keep dividing by larger numbers and you will get close to 0. That proves that actually dividing by infinity would equal 0. Same goes for negative numbers, and negative infinity. Now, this division works in reverse, as we’ve all been taught. 1/4=.25, right? We know that 1/.25 also equals 4. Therefore, since X/∞=0, and X/-∞=0, X/0=∞ and -∞

Yes, you divide by 0 and get 2 imaginary numbers. Though, 0 is imaginary itself, and is neither a negative or positive number. This is true even when 0 is divided by 0, it can’t come out as 1 in that case.

Last edited Jun 09, 2011 at 11:23AM EDT
Jun 09, 2011 at 11:16AM EDT
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This was the best picture I could find to address the situation. Amazing find btw. TELL THE MATHEMATICIANS OF THE WORLD!

Jun 09, 2011 at 11:29AM EDT
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Katie C. wrote:

Ok, so you know how everyone tried to do it? I finally succeeded.

It hit me in Calculus class about a week ago.
So, in calc, where reciprocals are concerned, as x approaches 0, y approaches infinity? But it’s also true that as x approaches infinity, y approaches 0.

Graph:

In that case, anything divided by infinity will be 0. Take out a calculator and witness this effect: Keep dividing by larger numbers and you will get close to 0. That proves that actually dividing by infinity would equal 0. Same goes for negative numbers, and negative infinity. Now, this division works in reverse, as we’ve all been taught. 1/4=.25, right? We know that 1/.25 also equals 4. Therefore, since X/∞=0, and X/-∞=0, X/0=∞ and -∞

Yes, you divide by 0 and get 2 imaginary numbers. Though, 0 is imaginary itself, and is neither a negative or positive number. This is true even when 0 is divided by 0, it can’t come out as 1 in that case.

Yup, as I’ve said before, in Calculus, you will explore the concept of division by zero. Sometimes, the answer’s not even undefined.

Jun 09, 2011 at 12:14PM EDT
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The problem with that is that it still isn’t dividing by zero.

It is dividing as the limit approaches zero, which although very close to zero, still isn’t zero.

Jun 09, 2011 at 12:19PM EDT
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Alllllright! Lets try this here!

take a 0 and Quiet mumbling Divide it by that, Moar mumbling Aaaaand we get!

Uhhh. Wait I th- Errr, is it normal for the calculator to start implo- Oh bawls!!!

Jun 09, 2011 at 12:31PM EDT

Chris wrote:

The problem with that is that it still isn’t dividing by zero.

It is dividing as the limit approaches zero, which although very close to zero, still isn’t zero.

I’m dividing by zero on paper.

Jun 09, 2011 at 01:47PM EDT
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You don’t need all that fancy-schmancy calculus stuff to understand the concept.
You could actually think of it as a word problem!
For example, I have an object that takes up exactly 8 cubic centimeters. Whatever you divide by, you are saying “there is exactly this much of this in this”, so if you divide by 4 you can say there is exactly 2 units of 4 cubic centimeters in an 8 cubic centimeter object. If you divide 1 by 0, you are asking how much nothing is in something. Therefore, I conclude that there is actually MORE than infinite nothing in something, since 0=nothing, and 0=/=X (when X=/=0). So X/0=∞+X. If you subtract X from both sides, you get 0=∞. BUT since infinity=0, then X-X=∞. When you multiply both sides by ~1, you get ~X-~X=~∞. Since subtracting a negative # equals adding the #, you get -X+X=-∞, and since anything minus itself=0, it can be further simplified to 0=-∞.
So with that logic, 0 DOES in fact equal both ∞ and -∞.
Who would’ve thought a dividing by zero thread would be so much fun?

Last edited Jun 09, 2011 at 06:13PM EDT
Jun 09, 2011 at 06:06PM EDT
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Note: I had to change some of the -‘s to ~’s b/c they were producing textile strikethroughs.
Dear princess Celestia, today I divided by 0.

FFFFFFFFFFFFUUUUUUUUUUUUUUUUUUUUUUU

Last edited Jun 09, 2011 at 07:31PM EDT
Jun 09, 2011 at 06:09PM EDT
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5 Devided by 0= 5, since it was not really devided it remains at 5, so its not deviding.

Jun 09, 2011 at 09:30PM EDT

Sweatie Killer wrote:

5 Devided by 0= 5, since it was not really devided it remains at 5, so its not deviding.

You do understand, that you are perfectly correct, right?

Jun 10, 2011 at 04:04AM EDT
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Sweatie Killer wrote:

5 Devided by 0= 5, since it was not really devided it remains at 5, so its not deviding.

5 divided by 1 is 5. This thread is about the theoretical concept of dividing by zero, which we all learned in kindergarten is impossible. Also,

INCORRECT SPELLING; YOUR STATEMENT IS INVALID!

Jun 10, 2011 at 11:22AM EDT
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Division by 0 is fairly easy to understand.
Let’s assume, that you want to divide 5 by 0. In that case, you must find a number by which you must multiply 0 in order to get 5. And since every single number multiplied by 0 is 0…
But even if we assume, that infinity * 0 isn’t equal to 0, we get infinity * 0 = 5.
But why 5? No matter what number you multiply or divide infinity by, you always get infinity- it just makes the said infinity bigger or smaller, yet still infinite (… kinda hard to explain that one). So, since we’re assuming 0 * infinity = infinity, then if you divide 5 by 0, you might get infinity. But, every division must be reversable, and 0 * infinity is, like I said, infinity. And if it isn’t, then it must be 0. So, division by 0 is invalid, even if you try to use infinity to help you out.
Duh.

Last edited Jun 10, 2011 at 11:56AM EDT
Jun 10, 2011 at 11:55AM EDT
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You need to be really careful dividing by zero because there a lot of counterintuitive, paradoxical results you can get if you don’t know what you’re doing.

In general, in the limit of n approaches 0
X/n can equal ∞ or -∞.

One of the reasons why you can’t divide by zero is very simple:
8*x=8 | x = 1
8*x=0 | x = 0
0*x=0 | x = infinite amount of solutions.

0/0 is feasible in some situations, if you think about it in limits (not really division by zero, but close).

for the limit as x → 0:

(5x^2)/(2x^2)

apply l’hopital’s rule and find the derivative of the top and bottom of the fraction.

(10x)/(4x)

Take the derivative until (lim x → 0) isn’t 0/0.

10/4 = 0/0.

You can also use l’hopital’s rule for ∞/∞

Another example of this is this famous mathematical fallacy:

The last step is erroneous because (a-b)/(a-b) = 0/0, and therefore you can get some pretty fucked up results if you don’t do it right.

However, if you think Division by Zero = ±∞ will work in any case where zero isn’t dividing by itself, you need to be really careful.

As Takuanuva noted, you used x/∞=0 to justify x/0=∞. But what about ∞*0=x?

You can do it sometimes, but you need to reapply l’hopital’s rule, and make the equation a 0/0 or ∞/∞ situation:

For example:

for the limit as x → 0:

(5x^2)(7/(x^2))
Which is equivalent to:
0*∞

So set up the eqauation, so that instead of multiplying, you divide by the reciprocal:

(5x^2) / ((x^2)/7)
or
0/0

so taking the derivative…

lim x → 0
(10x)((2/7)x)
lim x → 0
(10)/(2/7)
=35

So unlike what Takuanuva said, 0*∞ does not always equal ∞ or 0, although it more than often does.

tl;dr: division by zero is sometimes possible, but you need to use limits (which isn’t really strictly dividing by zero, but as close as you can get). And you need to define 0 or ∞ as positive, one-sided, both-sided, negative, undefined- depending on the situation.

lim → 0+: 1/x = ∞
lim → 0-: 1/x = -∞

There are also other ways to “divide by zero,” but you can’t do it in the same way you’d divide by any other real number, and even using limits, you’re not strictly dividing by zero, only getting close to it.

Also, although I said, “x=∞” to illustrate a point, its not proper because ∞ is not a value, and so nothing actually “equals infinity,” and with the problems of paradoxes, infinite solutions, and no solutions- you can’t really use infinity in an equation the same way you’d use real values, meaning that division by zero in its strictest sense is impossible.

So the general rule is: when you divide by zerOH GOD WHAT’S HAPPENING

Last edited Jun 10, 2011 at 12:38PM EDT
Jun 10, 2011 at 12:15PM EDT
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Quick summary about how to divide by 0:
You can’t*. Ever.
Now you know. And knowing is half the battle.

*Unless your name is Chuck Norris or Cave Johnson.

Last edited Jun 10, 2011 at 02:13PM EDT
Jun 10, 2011 at 02:02PM EDT
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Well, it is belived, that succesfully dividing by 0 produces infinite amounts of energy.
Which would be either used to:
a) Remove the fossil fuels from our life by having a generator that divides by 0, thus produces infinite power
b) Remove the fossil fuels from our life by turning the entire earth/solar system/galaxy/universe/multiverse into fine dust with one simple equation

Last edited Jun 10, 2011 at 03:03PM EDT
Jun 10, 2011 at 03:02PM EDT
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Takuanuva wrote:

Well, it is belived, that succesfully dividing by 0 produces infinite amounts of energy.
Which would be either used to:
a) Remove the fossil fuels from our life by having a generator that divides by 0, thus produces infinite power
b) Remove the fossil fuels from our life by turning the entire earth/solar system/galaxy/universe/multiverse into fine dust with one simple equation

b) -> Seems like a great solution to the overpopulation problem!

Jun 10, 2011 at 04:12PM EDT
Quote

Ogreenworld wrote:

You need to be really careful dividing by zero because there a lot of counterintuitive, paradoxical results you can get if you don’t know what you’re doing.

In general, in the limit of n approaches 0
X/n can equal ∞ or -∞.

One of the reasons why you can’t divide by zero is very simple:
8*x=8 | x = 1
8*x=0 | x = 0
0*x=0 | x = infinite amount of solutions.

0/0 is feasible in some situations, if you think about it in limits (not really division by zero, but close).

for the limit as x → 0:

(5x^2)/(2x^2)

apply l’hopital’s rule and find the derivative of the top and bottom of the fraction.

(10x)/(4x)

Take the derivative until (lim x → 0) isn’t 0/0.

10/4 = 0/0.

You can also use l’hopital’s rule for ∞/∞

Another example of this is this famous mathematical fallacy:

The last step is erroneous because (a-b)/(a-b) = 0/0, and therefore you can get some pretty fucked up results if you don’t do it right.

However, if you think Division by Zero = ±∞ will work in any case where zero isn’t dividing by itself, you need to be really careful.

As Takuanuva noted, you used x/∞=0 to justify x/0=∞. But what about ∞*0=x?

You can do it sometimes, but you need to reapply l’hopital’s rule, and make the equation a 0/0 or ∞/∞ situation:

For example:

for the limit as x → 0:

(5x^2)(7/(x^2))
Which is equivalent to:
0*∞

So set up the eqauation, so that instead of multiplying, you divide by the reciprocal:

(5x^2) / ((x^2)/7)
or
0/0

so taking the derivative…

lim x → 0
(10x)((2/7)x)
lim x → 0
(10)/(2/7)
=35

So unlike what Takuanuva said, 0*∞ does not always equal ∞ or 0, although it more than often does.

tl;dr: division by zero is sometimes possible, but you need to use limits (which isn’t really strictly dividing by zero, but as close as you can get). And you need to define 0 or ∞ as positive, one-sided, both-sided, negative, undefined- depending on the situation.

lim → 0+: 1/x = ∞
lim → 0-: 1/x = -∞

There are also other ways to “divide by zero,” but you can’t do it in the same way you’d divide by any other real number, and even using limits, you’re not strictly dividing by zero, only getting close to it.

Also, although I said, “x=∞” to illustrate a point, its not proper because ∞ is not a value, and so nothing actually “equals infinity,” and with the problems of paradoxes, infinite solutions, and no solutions- you can’t really use infinity in an equation the same way you’d use real values, meaning that division by zero in its strictest sense is impossible.

So the general rule is: when you divide by zerOH GOD WHAT’S HAPPENING

Pretty cool, only a cannot equal b. In algebraic problems all letters stand for different numbers.
 
My God is with me and feels just fine.

Jun 10, 2011 at 05:57PM EDT
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Probably this has already been said… but you can’t divide by zero for a simple reason.
When you divide, you split a number up into groups. For example, five divided by five is splitting five into five groups, and each group is equal to 1.
So you can’t split a number up into zero groups. The number can’t just disappear, it has to be subtracted. If you successfully divided by zero, you would have fundamentally broken the laws of physics, which states that matter and energy can neither be created nor destroyed. I’m talking IRL, of course. Not on a calculator; if it divides by zero, its broken.

Jun 10, 2011 at 09:47PM EDT
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Skeletor-sm

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