HOW TO DIVIDE BY ZERO?!

I RLY WANNA KNOW

To 40, I don't know, it's my way of seeing it. A part of me is right and a part of you is right. The proof I made isn't really.. a proof, it's a way to show that..

0 * x does not equal 3  [zero times x (a number) always equal zero]

And when you or a calculator try to find it, there's no number that can find any number that can get the answer if you multiply a number by zero. You'll just.. have no answer to that, which can be put as "Undefined" or "Does Not Exist"

I may not be "teh" best at math explanations or being "teh" Win either.

Here's another explanation (or another way to be flamed at, depends) a bit more English oriented but, your call.

Anon Way

Take 3/0 as the example... It's like saying "You have 3 people but I want to split you guys into groups of eh.. GTFO ALL OF YOU" And it's like nothing happens, and they all go back to 4chan. Yay...

Math Way (Calculus)

lim      [f(x)-f(c)]/(x-c)
x->c

Given
f(x) = x^2 - 1
c = 2

If you plug in the equation as it is, without simplifying, you'd end up as:

x^2-4/(x-2)

On the denominator (x-2), you attempt to plug in c = 2, 2-2 = 0 and if your numerator is any number but zero... It will turn out "Undefined" (In this case, it's 4/0) And the purpose of finding limits is to know what point y is at when x APPROACHES that number. If this problem can't factor out, then it is truly "Undefined", but in this case, it can be factored.

End up simplified as:
(x + 2)(x - 2) / (x - 2)

The (x - 2)'s cancel out...
and 2 + 2 = 4

***Note : This math section shows a bit more than needed with the 'divide by zero' thing.


Just remember Anon...

10/5 = 2
0/0 = 0
3/0 = Undefined, Does Not Exist

>>41
"0/0 = 0" => False

I don't quite see what you're saying.  1/x is undefined at x=0, but how is (x^2-4)/(x-2) not "truly undefined" at x=2?  The only difference is that the graph of (x^2-4)/(x-2) looks exactly like the graph of (x+2), but there is a "hole" at x=2, where (x^2-4)/(x-2) is undefined.

And you'd think that since this is post #42, I'd have the Answer.  Sorry.  No dice.  Not even 20-sided.

One more thing:

"'You have 3 people but I want to split you guys into groups of eh.. GTFO ALL OF YOU' And it's like nothing happens, and they all go back to 4chan."

ZOMFGWTFLOLROFLMFAO!!!!!!!!!!

>>35
If one divides an object by -.5, one will now have -2 objects.

It is utter nonsense in real world! Yet still, 1/-.5 = -2, indeed.

Why is that? Because in math we use division operation in somewhat different sense than "slicing apples to pieces with a knife". Although the operation resembles the apple slicing when numbers involved are positive.

Introduce yourself to algebra to understand and appreciate operations on sets.

>>33
Which number base you're willing to talk about, and how is "/" defined in it?

division by zero is a concept, it cannot be numerically expressed.

For example, let's talk chemistry, a reaction occurs in equilibrium (i'm not bothered thinking of chemicals). At equilibrium, there are 0 moles of reactant and 1 moles of each product. This would mean that Kc would be the following equation ((1)(1))/((0)(0)). which goes down to 1/0. Some people would say that this is impossible and leave it in the dirt. However, since we know the context of this sum, we can say that Kc approaches infinity, because all the reactants will eventually react. This can be said for the other way, but i'm not going to say anymore on that than this.

>>43
We have great precedent for negative numbers.  Debits, for instance.  Hence, you fail.

>>44
When a reaction achieves equilibrium, generally the products don't disappear entirely.  There is always some -- however tiny -- amount of reactants being converted into the products again.  Hence, you too fail.

0/0 = x

0x = 0

0/0 = everything

ex.
0*1 = 0
0*1337 = 0



not infinity

>>46
You made the same mistake as a previous post, by treating 0/0 as equal to 1.  IF 0/0 would be equal to 1, THEN you could do that.  But that's not the case.  In fact, here's something that I just thought up:

Division by:
-(x>1) will move a number closer to Zero
-(x<-1) will move a number past Zero to a lesser absolute value than that of the original number
-(0<x<1) will move a number further away from Zero.
-(-1<x<0) will move a number past Zero to a number of greater absolute value than that of the original number.

Basically, the division patterns look like this:
-->(-1)<--(-0+)-->(+1)<--
Zero is neither positive nor negative.  What happens to the number it divides?

How about this.
http://mathforum.org/library/drmath/view/52400.html

When in the face of superior intellect, get a wizard.

>>44
Sorry man, but that violates the laws of conservation of energy.  You can't get less stuff out than what you put in.  It all had to go somewhere.  In other words, when your reactant is gone, you will be left with product, and a probable change in energy, assuming a closed system.  The ratio of reactant to product is a quantitative number describing the amount of reactant needed to produce an amount of product.  If you had no reactant, then you'd have no product.  n/0 in this case doesn't make sense.

But that's what this is about, making sense.  The sad fact is there is no known concept in which n/0 makes sense in a physical way, and in a theoretical way it is worked around or avoided as it makes no sense there either.  Until some phenomena exists where a ratio to nothing is desirable, it will continue to be avoided.

>>47
Isn't 0 considered to be positive, by definition?

>>50
gb2 high school. 0 is neither positive nor negative.

>>51
Oh, s'cuse me.
http://en.wikipedia.org/wiki/Negative_and_non-negative_numbers

"A number is non-negative if and only if it is greater than or equal to zero, i.e., positive or zero."

>>52

"The non-negative numbers are the real numbers that are not negative (they are positive or zero). The non-positive numbers are the real numbers that are not positive (they are negative or zero)."
Clearly there are three categories:  Positive, negative and zero.

>>51
By convention, zero is neither positive nor negative.  Similar to how 1 is neither prime nor composite.

Hmm.Take 5/0.

Let's call the answer c, plus r remainder.



a/b = c + r, abcr : {integers}

a = b*(c+r)

5 = 0*(c+r)

Now, this is a total contradiction. Even if (c+r) is INFINITELY BIG, 0*(c+r) will NEVER equal 5. You can't add 0 to itself infinite times. However 0.000000000(lots of zeroes)000001*(something else) will eventually become 5 if (something else) is big enough.

What about -5/0?

Now, -5/0 = 5/-0 = 5/0.

5 = 0*(c+r). c+r is approaching NEGATIVE infinity as b is approaching zero. (think y=5/x). 0 * negative large number = 5 ? Even more ridiculous.

Hope this sheds some light. Just think about it algebraically and it all makes sense (or in this case... very clearly doesn't make sense, which is what I wanted). Proof by contradiction - we started out assuming (c+r) was an integer, but no such integer solves 5 = 0*(c+r), therefore assumption is false, which is what we were trying to prove.

>>45
 Not always. E.g. ethanol + ethanoic acid = ethyl ethanoate and water. Let's assume that we have 1 mole of ethanol and 1 mole of ethanoic acid. Therefore we will have 1 mole of water and 1 mole of ethyl ethanoate. We'll also assume that this is in a closed system and that the reactant COMPLETELY react , forming the maximum yield of the products. Therefore, we will have the equation of ((1)(1))/((0)(0)). This can happen for some equiibrium equations as the amount of reatants is so small at equilirbium, it cannot be measured, so it is as good as 0.

>>49
Where are you coming from? Moles aren't a measure! Just of quantity. None of the elements were lost, albeit I was being vague about the actual reaction, but that doesn't really matter.  The n/0 is when the reaction is at EQUILIBRIUM, not initially. Taking the reaction I used before, I *initially* had 1 mole of each reactant, and they completely reacted to form 1 mole of each products, no reactant left. The numbers for the Kc formula are the concentrations (divided by the volumes, if a gas) of the produts at equilibrium and the concentration of the reactant.

>>55
Third post I've seen that makes the mistake of treating 0/0 as equal to 1.  THIS IS NOT TRUE!!!  In your formula, "a/b=c+r"

Here's a small fallacy to show what I mean:
Let a=b (given)
a^2=ab (multiply both sides by a)
a^2-b^2=ab-b^2 (subtract b^2 from both sides)
(a+b)(a-b)=b(a-b) (factor both sides appropriately)
a+b=b (divide both sides by (a-b))
a+a=a (substitute a for every instance of b, since a=b)
2a=a (combine like terms)
1=2 (divide both sides by a)

The problem here is dividing by (a-b).  I cannot do this becuase a=b, therefore a-b=0.  Since division by zero is undefined and is the topic of this thread, I'm not allowed to take (a-b) out of there, because it would be treating 0/0 as equal to 1.  Now then, if everyone would get ALL the errors out of their proofs next time, I'll be much happier.

BUMP!

0/0 = x
0x = 0
x = All numbers (since any number times 0 is 0)

>>59
YOU ARE A FUCKING MORON!  TRY READING THE THREAD BEFORE MAKING THE SAME MISTAKE AS AT LEAST 100 OTHER MORONS!  0/0 =/= 1.  IF 0/0 = 1, THEN multiplying both sides of the first expression by 0 would yield the second line.  Try analyzing your validity before raping your crediblity!

>>60
Don't feed the trolls, dude. Anonymous has no credibility.
This thread has outlived its usefulness.

>>60
I didn't say 0/0 = 1.

1. 0/0 = x
-We don't know what 0/0 is, so we make it equal to x and solve for x.

2. (0/0)*0 = x*0
  0 = 0x
-Multiply both sides by 0

3. 0 = 0
-Any number times 0 is 0

4. x = R

>>62
ah, flawless logic

x = 1/2
(1/2)*0 = 0x
0 = 0x
x = R

nice.

>>62
ITT highschoolers who think they know anything at all about mathematics.

In 0x=0, x would simply be "all real numbers", right?

>>65
As has been said a million times before in this very thread, yes. Learn to read.

>>65
Why stop there?  What about 0*3i?  or 0*i for that matter?  Why not just all numbers?

>>62
Yes, you did assume that 0/0 = 1.  That's what validates multiplying both sides by any other denominator.  If 3/4 = x, then multiplying both sides by 4 yields 4*3/4 = 4*x.  The fours on the left side CANCEL OUT BECAUSE 4/4 = 1.  But the same does not apply to doing this with zero, since 0/0 does not, by convention, equal 1.

>>64
Yeah, probably.

>>65
0*3i is 3i. Oi*3i, on the other hand...

>>68
...
>>67 is right, 0*i equals 0, and x would be equal to ℂ.

lol 69....
Seriously, >>69, thank you for knowing math.  We need people like you in this thread.

Trolls, move to /b/, plox.
There you can easily generate 500 reply threads on moronic subjects like: division by zero, 0.9999... = 1 and matter state of glass.
Those are boring here. Actually, you only troll each other.

you know, its pretty easy to divide by 0, you just have to do almost the same thing that people responsible for math/numbers convention do the past xxxx years, in other words dividing by 0 or any other operation between numbers is just like it is because some1 said its logical and prooved it :D, u c there is your chance to get a nobel ^^ gogogo

>>72
lrn2spell 'you' and 'see'.  Your post was boring.

I was going to mention limits (especially since differential calculus, arguably, relies on division by zero using them) but I see that's already been covered.

>division by zero, 0.9999... = 1 and matter state of glass.
Undefined, True, and Liquid.
</thread>

>>75
You wish. Glass is an amorphous solid.

everything flows over long enought with enough gravity

The "slow liquid" state of glass is largely an urban myth.  The indicators of flow have been mis-interpreted.  Glass is indeed an amorphous solid.

For "slow liquids", look up the pitch drop experiment in England.  It was started in 1927, and the pitch sample drips 1 drop about every 10 years:

http://en.wikipedia.org/wiki/Pitch_drop_experiment

>>76
">Glass is an amorphous solid."
Solids, by definition, hold a shape.  Glass flows.  Granted, it takes hundreds of years to be significant, but it flows.  You lose.

>>77, Glass flows.  Stone does not.  Stone is solid.  Glass is liquid.  Solids do not flow.  Solids do not even permanently deform except for extremely large forces.

>>78
That article says that pitch is highly viscous fluid.  Glass is the same way, except apparently about ten times thicker.

All solids "flow", dipshit. Glass has a flow time of 10^32 years (not "hundreds") at room temperature, making it a fuck of a lot less viscous than most things people consider solid.