Do you think we'll ever have a computer powerful enough to divide by 0?

[Legendary_Bibo]

I'm sure there's some crazy mathematical proof that can be ran by a computer rather than just having it avoid the issue.

[Tristam Green]

Division by zero is impossible.

[Phrea]

It's possible, it just doesn't change anything.

Next up: how do magnets work? ;)

[Legendary_Bibo]

Perhaps a sun is just an extremely powerful computer that produces a lot of heat, and when it divides by zero it turns into a black hole...

[PurposeOfReason]

Perhaps a sun is just an extremely powerful computer that produces a lot of heat, and when it divides by zero it turns into a black hole...
No. What do they teach kids these days? It's not hard, division by zero is not possible. It'd also be darn hard to make a computer to solve something we don't understand or we would know a whole lot more. The computer is only as smart as we make it. At least until a learning AI comes along, if ever.

[lisati]

Well.... there are ways of representing the square root of -1. No doubt someone will come up with a way of representing division by zero that won't trip things up.

[RiceMonster]

Division by zero is impossible.

Unless you're Chuck Norris.

[Phrea]

Unless you're Chuck Norris.

Gheheh, he just had to come up at some point. :D

[McRat]

They covered that in Calculus, but I drank those brain cells away many years ago. It's not infinity, nor zero.

It seems many CPU/MPU's? have look-up tables for division, so it justs reports an error.

Remember when the first batch of Pentiums had an error in the look-up tables and got some math problems wrong? I still have one of the keychain Pentiums from that release somewhere.

[lisati]

They covered that in Calculus, but I drank those brain cells away many years ago. It's not infinity, nor zero.
That's stirred up a few recollections from many years ago. :)

[wojox]

No and Don't try this at home.

http://halshop.files.wordpress.com/2007/03/phpw9jvl0pm.jpg

[Legendary_Bibo]

No. What do they teach kids these days? It's not hard, division by zero is not possible. It'd also be darn hard to make a computer to solve something we don't understand or we would know a whole lot more. The computer is only as smart as we make it. At least until a learning AI comes along, if ever.

bah. I learned the proof and stuff in calculus. I'm just letting my imagination run wild. Black holes are caused from nature dividing by zero.

[Random_Dude]

You can't divide by zero because you would reach infinite.

The lim costant/x when x tends to zero, is equal to infinite.
For example, try to calculate this divisions:

1/1
1/0.1
1/0.01
1/0.001
1/0.0001
1/0.00001
1/0.000000000000000000000000001

You will notice that it tends to greater numbers, it is impossible to get an precise number when you divide by zero. The best thing you can say is that the result tends to infinite when the denominator tends to zero.

I hope that explains it.;)

Cheers :cool:

[cap10Ibraim]

I remember something from a math course about rings and number theory
It's about the set of elements and the operations you define on this set
there are some cases - groups , rings where you define a division by zero

[Sporkman]

The division operation for real numbers is not defined for a denominator of zero.

So, the result of 1/0 is not defined. It is not infinity.

[jrothwell97]

bah. I learned the proof and stuff in calculus. I'm just letting my imagination run wild. Black holes are caused from nature dividing by zero.

No.

Division by zero is simply undefined, and therefore has no value.

x / 0 equals nothing, not even zero: it's like "250 / Walnuts" or "∫2x+3 (Captain Picard)"

[donkyhotay]

2x+3 (Captain Picard)"

what do you mean it makes no sense? The answer of course is: 3x^(7 of 9)! (c;

[Sporkman]

x = 5
x^2 = 25
x^2 - x = 25 - x
x^2 - x - 20 = 25 - x - 20
x^2 - x - 20 = 5 - x
(x - 5)(x + 4) = 5 - x
(x - 5)(x + 4)/(x - 5) = (5 - x)/(x - 5)
x + 4 = -1
x + 4 - 4 = -1 - 4
x = -5

Therefore: 5 = -5.

[Bachstelze]

Well.... there are ways of representing the square root of -1.

No. There are numbers that, when multiplied by themselves, give -1 as a result. This is different. The square root function is defined only for positive real numbers.

[purelinuxuser]

We already have a computer that can divide by 0, it's Firefox 3.6! Paste this into your address bar:

javascript: alert(5000 / 0);
Firefox will say Infinity! :)

[Random_Dude]

x = 5
x^2 = 25
x^2 - x = 25 - x
x^2 - x - 20 = 25 - x - 20
x^2 - x - 20 = 5 - x
(x - 5)(x + 4) = 5 - x
(x - 5)(x + 4)/(x - 5) = (5 - x)/(x - 5)
x + 4 = -1
x + 4 - 4 = -1 - 4
x = -5

Therefore: 5 = -5.

Lol good argument.

(x-5)=0, therefore if you could divide by zero you could do this step (x - 5)(x + 4)/(x - 5) = (5 - x)/(x - 5)
Which would result in 5=-5

[jerenept]

No. There are numbers that, when multiplied by themselves, give -1 as a result. This is different. The square root function is defined only for positive real numbers.

The method of negative square roots involves imaginary #s

Check Wikipedia, I think it is there.

[Bachstelze]

The method of negative square roots involves imaginary #s

Check Wikipedia, I think it is there.

Then we're not discussing square root as a function, since it has two possible results. The post I quoted said "the square root", implying it is unique.

[purelinuxuser]

x = 5
x^2 = 25
x^2 - x = 25 - x
x^2 - x - 20 = 25 - x - 20
x^2 - x - 20 = 5 - x
(x - 5)(x + 4) = 5 - x
(x - 5)(x + 4)/(x - 5) = (5 - x)/(x - 5)
x + 4 = -1
x + 4 - 4 = -1 - 4
x = -5

Therefore: 5 = -5.

Actually, I think that's an extraneous solution ;)

In fact, if you solve it this way...

x^2 = 25
x^2 - x = 25 - x
x^2 - x - 20 = 25 - x - 20
x^2 - x - 20 = 5 - x
x^2 - x - 20 + x = 5 - x + x
x^2 - 20 = 5
x^2 - 20 + 20 = 5 + 20
x^2 = 25
x = 5

You'll find that 5, does in fact, equal 5 :)

[Sporkman]

http://imgs.xkcd.com/comics/principle_of_explosion.png

[Sporkman]

Actually, I think that's an extraneous solution ;)

In fact, if you solve it this way...

x^2 = 25
x^2 - x = 25 - x
x^2 - x - 20 = 25 - x - 20
x^2 - x - 20 = 5 - x
x^2 - x - 20 + x = 5 - x + x
x^2 - 20 = 5
x^2 - 20 + 20 = 5 + 20
x^2 = 25
x = 5

You'll find that 5, does in fact, equal 5 :)

No, 5 = -5. I proved it. In the universe bounded by this thread, division by zero is defined and 5 = -5.

[sisco311]

The method of negative square roots involves imaginary #s


Aren't real numbers imaginary too?

[Sporkman]

Actually, I think that's an extraneous solution ;)

In fact, if you solve it this way...

x^2 = 25
x^2 - x = 25 - x
x^2 - x - 20 = 25 - x - 20
x^2 - x - 20 = 5 - x
x^2 - x - 20 + x = 5 - x + x
x^2 - 20 = 5
x^2 - 20 + 20 = 5 + 20
x^2 = 25
x = 5

You'll find that 5, does in fact, equal 5 :)

Actually, now that you mention it, your last step is wrong - it should be:

x = 5 or -5

[lisati]

No. There are numbers that, when multiplied by themselves, give -1 as a result. This is different. The square root function is defined only for positive real numbers.
I'm assuming here that you're not being sarcastic or trying to be funny.

There is away of representing the square root of -1, even if you can't calculate it. It's called "i" (standing for "imaginery number (http://en.wikipedia.org/wiki/Imaginary_number)"), or, if you're an electrical engineer, it's called "j".
Whenever you're doing a calculation that calls for the square root of -1, you plug in the letter "i" and proceed with your calculation. Later, if you're doing things properly, you'll end up with something like i^2, at which point you replace it with -1.

There are also what's known as "complex numbers (http://en.wikipedia.org/wiki/Complex_number)".

[Sporkman]

Aren't real numbers imaginary too?

No, but they are complex numbers with a zero imaginary component.

[sisco311]

No, 5 = -5. I proved it. In the universe bounded by this thread, division by zero is defined and 5 = -5.

Bah!

x=5 => x^2=25 but x^2=25 <=/=> x=5

[mmix]

I would like to link Riemann zeta function.
http://en.wikipedia.org/wiki/Riemann_zeta_function

[sisco311]

No, but they are complex numbers with a zero imaginary component.

A number is a mathematical object, an abstract object which does not exist at any particular time or place. Is something like this real? :)

[StephenF]

You can't divide by zero because you would reach infinite.

The lim costant/x when x tends to zero, is equal to infinite.
For example, try to calculate this divisions:

1/1
1/0.1
1/0.01
1/0.001
1/0.0001
1/0.00001
1/0.000000000000000000000000001

You will notice that it tends to greater numbers, it is impossible to get an precise number when you divide by zero. The best thing you can say is that the result tends to infinite when the denominator tends to zero.

I hope that explains it.;)

Cheers :cool:
But:

1/-0.000000000000000000000001
Tends towards greater negative numbers as you approach zero from the negative side. Since zero is neither positive nor negative is the infinity positive or negative for a division by zero?

[sydbat]

And all these years I thought that 2 + 2 = 22! My brain hurts...

[lisati]

But:

1/-0.000000000000000000000001
Tends towards greater negative numbers as you approach zero from the negative side. Since zero is neither positive nor negative is the infinity positive or negative for a division by zero?

<aside>This thread is taking me back to my high-school/college and university days. </aside>
Making a graph of this sort of thing can be interesting, with larger negative numbers as you approach zero from the negative side, and larger positive numbers as you approach from the positive side. The word asymptote (http://en.wikipedia.org/wiki/Asymptote) comes to mind.....

[McRat]

Actually, now that you mention it, your last step is wrong - it should be:

x = 5 or -5

When write code to solve geometric problems, this is a common issue. You forget to solve for both directions. It bites you when you are working in multiple quadrants. And because of the way some computers do floating point decimal math, sometimes there is a very small gap between the two solutions, which creates a gap in geometry. In other words, it might solve out at:

X = -4.999999999999
X2 = 5.000000000000

It has something to do with binary math never being perfect for doing decimal notation. You need to use binary-coded decimal libraries if you want no gaps.

[Legendary_Bibo]

x = 5
x^2 = 25
x^2 - x = 25 - x
x^2 - x - 20 = 25 - x - 20
x^2 - x - 20 = 5 - x
(x - 5)(x + 4) = 5 - x
(x - 5)(x + 4)/(x - 5) = (5 - x)/(x - 5)
x + 4 = -1
x + 4 - 4 = -1 - 4
x = -5

Therefore: 5 = -5.

This is faulty math. x can equal 5 or -5. It doesn't state that 5=-5
Go back to Algebra ;)

[NovaAesa]

Divide 2 IEEE floating points where the second is 0 and it results in NaN. Not much computer power required to do it :P

[lisati]

This is faulty math. x can equal 5 or -5. It doesn't state that 5=-5
Go back to Algebra ;)

We are told at the start that x=5, so x != -5; the "mistake" lies in something in the working that relates to the title of the thread......

See if you can spot a similar mistake in the following example:

Start with: a=b
Multiply by a: a^2=ab
Subtract b^2: a^2-b^2=ab-b^2
Factorize: (a+b)*(a-b)=b*(a-b)
Divide by a-b: (a+b)*(a-b)/(a-b)=b*(a-b)/(a-b)
Simplify: a+b=b
But a=b, so: a+a=a
So: 2*a=a
Divide by a: 2*a/a=a/a
Simplify: 2=1

[The Real Dave]

Currently, we human don't understand how to divide something by nothing. We just can't wrap our heads around it.

Computers are coded by humans, and so, are generally about as smart as we are. The problem can be solved by using computer AI which evolves and teaches itself, which exists, but is generally used for commercial products, refining a product by evolutionary means to create the "perfect" product, depending on the inserted variables.

So it's possible that something else could figure it out for us. Whether we could understand the results it gives us? Thats another question.


That and, people seem to be afraid of evolving computers. ;)

[lisati]

I envisage that we might end up using a "dodge" analogous in some way to the previously mentioned imaginery number "i". It would, however, probably take a different form.

[JDShu]

The math geeks back in my high school showed me the 1 = -1 argument. I just thought they were being lame :P

[Legendary_Bibo]

We are told at the start that x=5, so x != -5; the "mistake" lies in something in the working that relates to the title of the thread......

See if you can spot a similar mistake in the following example:

Start with: a=b
Multiply by a: a^2=ab
Subtract b^2: a^2-b^2=ab-b^2
Factorize: (a+b)*(a-b)=b*(a-b)
Divide by a-b: (a+b)*(a-b)/(a-b)=b*(a-b)/(a-b)
Simplify: a+b=b
But a=b, so: a+a=a
So: 2*a=a
Divide by a: 2*a/a=a/a
Simplify: 2=1

after you simplify you should subtract b from both sides then you have a=0 which means b=0 so for this problem the idea holds true. This also works for what you got because 0/0 is still undefined, and any scalar value is meaningless. The mistake is that you're claiming 0/0=1 which in fact it does not. I actually had to think about that one :D

[Legendary_Bibo]

The math geeks back in my high school showed me the 1 = -1 argument. I just thought they were being lame :P
I used calculus to get people to stop asking me stupid question when I tutored them with their geometry. For example, I was asked where the equation for a sphere came from. Just toss up the solid of revolution integral and bam! you've blown their minds. To them it looks complicated, to people who've taken calc it's rather simple.

[new_tolinux]

I don't get why it should be impossible.....

As I learned years ago:
10*0=0
3*4=12

Therefore:
12/4=3 and 12/3=4

So:
10/0=0

[lisati]

after you simplify you should subtract b from both sides then you have a=0 which means b=0 so for this problem the idea holds true. This also works for what you got because 0/0 is still undefined, and any scalar value is meaningless. The mistake is that you're claiming 0/0=1 which in fact it does not. I actually had to think about that one :D

Go up a line or two. In this example we're dividing by a-b, which means, because we start with a=b, we are dividing by zero. That is the "mistake" in the working.

edit: the example I was using was a restatement of this: http://mathforum.org/library/drmath/view/55792.html

[Sporkman]

<aside>This thread is taking me back to my high-school/college and university days. </aside>
Making a graph of this sort of thing can be interesting, with larger negative numbers as you approach zero from the negative side, and larger positive numbers as you approach from the positive side. The word asymptote (http://en.wikipedia.org/wiki/Asymptote) comes to mind.....

Attached: graph of 1/x

[Sporkman]

This is faulty math. x can equal 5 or -5. It doesn't state that 5=-5
Go back to Algebra ;)

Nope - I proved quite clearly that x = 5 and x = -5. Therefore 5 = -5.

Go back to arithmetic. ;)

[Sporkman]

we are told at the start that x=5, so x != -5; the "mistake" lies in something in the working that relates to the title of the thread......

See if you can spot a similar mistake in the following example:

Start with: A=b
multiply by a: A^2=ab
subtract b^2: A^2-b^2=ab-b^2
factorize: (a+b)*(a-b)=b*(a-b)
divide by a-b: (a+b)*(a-b)/(a-b)=b*(a-b)/(a-b)
simplify: A+b=b
but a=b, so: A+a=a
so: 2*a=a
divide by a: 2*a/a=a/a
simplify: 2=1

8)

[standingwave]

And all these years I thought that 2 + 2 = 22!No, but:

Reduce the expression: 16/64
Cancel the sixes: 16/64 = 1/4

Reduce the expression: 19/95
Cancel the nines: 19/95 = 1/5

[new_tolinux]

No, but:

Reduce the expression: 16/64
Cancel the sixes: 16/64 = 1/4

Reduce the expression: 19/95
Cancel the nines: 19/95 = 1/5
Won't work in:
26/62
or
39/93

[Legendary_Bibo]

Won't work in:
26/62
or
39/93

still you have to admit, that's a neat trick. You learn something new everyday!

[Legendary_Bibo]

Nope - I proved quite clearly that x = 5 and x = -5. Therefore 5 = -5.

Go back to arithmetic. ;)

There's a difference between 'and' and 'or'.
Go back to english. ;)

[Sporkman]

There's a difference between 'and' and 'or'.
Go back to english. ;)

Neither "and" nor "or" were in my proof (though "or" was part of my "Therefore" I suppose)...

Go back to...uh.......

[lisati]

We seem to have been side-tracked somewhat with this thread.....

[Legendary_Bibo]

We seem to have been side-tracked somewhat with this thread.....
Don't close it please. I'm rather enjoying these math discussions/arguments. I don't know any other intellects who like to discuss such matters. :D

[lisati]

Don't close it please. I'm rather enjoying these math discussions/arguments. I don't know any other intellects who like to discuss such matters. :D

No immediate plans to close this thread.....

[Cathhsmom]

Perhaps a sun is just an extremely powerful computer that produces a lot of heat, and when it divides by zero it turns into a black hole...

I am just now reading this thread and this just hit my funny bone. Great one!!

[sisco311]

We seem to have been side-tracked somewhat with this thread.....

I don't think that's possible.

[Tibuda]

Neither "and" nor "or" were in my proof (though "or" was part of my "Therefore" I suppose)...

Go back to...uh.......

that was not a "proof" that 5 = -5.

x = 5
x^2 = 25
x^2 - x = 25 - x
x^2 - x - 20 = 25 - x - 20
x^2 - x - 20 = 5 - x
(x - 5)(x + 4) = 5 - x
here you have just prooved that x=5 is a solution for x^2 - x - 20 = 5 - x


x^2 - x - 20 = 5 - x
(x - 5)(x + 4) = 5 - x
(x - 5)(x + 4)/(x - 5) = (5 - x)/(x - 5)
x + 4 = -1
x + 4 - 4 = -1 - 4
x = -5
and here you prooved that another solution for x^2 - x - 20 = 5 - x is x=-5

[Sporkman]

that was not a "proof" that 5 = -5.


Yes it was, assuming that division by zero is a valid operation.


here you have just prooved that x=5 is a solution for x^2 - x - 20 = 5 - x


Nope. I established that x = 5 as a premise of the argument. The above equation follows from that premise.


and here you prooved that another solution for x^2 - x - 20 = 5 - x is x=-5

No - I proved that, given the premise x = 5, x = -5. Therefore 5 = -5.

[standingwave]

Won't work in:
26/62
or
39/93It works 100% of the times when it works:
26/65 = 2/5
49/98 = 4/8

199/995 = 1/5
742/424 = 7/4
654/545 = 6/5
484/847 = 4/7
499/998 = 4/8
166/664 = 1/4
266/665 = 2/5

[undecim]

Division by zero doesn't work.

Why?

Short answer:

If x=y/z then y=z*x.

Therfore, if x=1/0, then 1=0*x, and there is no number that when multiplied by 0 is equal to -1.

Moreover, multiplication is commutative and associative, which means it doesn't matter what order your multiply numbers in, so suppose there was a number (lets call it "w") that when multiplied by 0 was equal to 1. In that case, w*0*10=10, right? But only if you multiple 0 and w first. If you multiple like w*(0*10), then you get 1! That gives us a contridiction. And since the only new assumption we have is that 1/0=w, that assumption must be wrong, since it leads to a contridiction.

Further explanation:

The reason mathemeticians originally found the need to use imaginary numbers was because there was no solution for the quadratic equation for a=1,b=0,c=1 (x^2 + 0x + 1 = 0 or x^2 + 1 = 0)

Guass (I think...) proved that with the square root of -1, you can solve not only that, but any algebraic equation of any order. That's why we can use "i" to represent the square root of -1.

The reason we can't make up a number to represent 1/0 is because there is no algebraic equation that requires it. As a direct result or that, 1/0 is not a number.

[Hyporeal]

Computers do divide by zero. It has already been said that some computer processes use NaN ("Not a Number") when dividing by zero. Therefore these processes use an algebra in which division by zero is allowed, and does not abort the computation.

But that is not what we mean when we speak of dividing by zero. We want to retain the useful properties of division, not resort to what amounts to an error code. For example:

A) 0/0 = 1
B) 0^2/0 = 0
C) (1-0^2)/(0+0^2) - 1/0 = -1

Unfortunately, (A) and (B) above appear to have contradictory notions of what 0/0 ought to be. Therein lies the source of contradictions in derivations that utilize division by zero in this way.

Fortunately, division by zero is not a new concept and has been solved, to a certain extent. Newton realized that he needed infinitely small values for his calculus, so he introduced special variables to stand for zero and performed algebra similar to (A), (B), and (C) above. Today we choose to formalize calculus with limits, but directly manipulating infinitesimals gives the correct results as well. Here's a correct version of Sporkman's derivation, with "h" as the infinitesimal part of x (so h effectively equals zero) :

x = 5 + h
x^2 = 25+ 10h + h^2
x^2 - x = 25 + 10h + h^2 - x
x^2 - x - 20 = 25 + 10h + h^2 - x - 20
x^2 - x - 20 = 5 + 10h + h^2 - x
(x - 5)(x + 4) = 5 + 10h + h^2 - x
(x - 5)(x + 4)/(x - 5) = (5 - x)/(x - 5) + (10h + h^2)/(x - 5)
x + 4 = -1 + (10h + h^2)/(x - 5)
x + 4 = -1 + (10h + h^2)/h
x + 4 = -1 + 10 + h
x + 4 = 9 + h
x = 5 + h

For a rigorous definition suitable for use in computers, consider the Hyperreal numbers (from which my forum name was back-constructed).

[new_tolinux]

Edit: never mind

[YuiDaoren]

For all you wonderful math geeks:

http://www.youtube.com/watch?v=CIJ0CikId8E

[Shining Arcanine]

Well.... there are ways of representing the square root of -1. No doubt someone will come up with a way of representing division by zero that won't trip things up.

Ask and thou shall receive:

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

[jflaker]

fractions
1/1 or 2/2 etc = 1 but 0/0 is NOT 1 and 1/0 is such a infinite 1 of 0 parts is not definable and is false as you can not have a part of nothing.

[mmix]

only i have to say is that we are all physical things which is belongs to electron & atom, i.e. nature.

[Legendary_Bibo]

only i have to say is that we are all physical things which is belongs to electron & atom, i.e. nature.
wait...what?

[mmix]

my thought about mathematics.

[Timmer1240]

If you divide something by zero then your not dividing it!So WHATS THE POINT!Good answer to a silly question!

[sxmaxchine]

dividing by zero is impossible

[Legendary_Bibo]

I'm loving this site haha
http://xkcd.com/435/

[blackcobra]

To divide by zero is imposible to define even by a computer

lim (y/x) = L
x->0

on the real number line,

lim => (means implies) we get closer and closer to 0.
x->0

(ie. 1/0.1=10, 1/0.01=100 , ... , 1/0=infintiy)

=> L=infinity

infinity cannot defined on the real line as there is no `max` or `sup` (Subject: Real Line Analysis).

A way of think about it. "Imagine we have an orange and the value of the orange is 75p and divided the orange by 0" say we divided it by 1/2, orange = 1.50 (half the orange and each half is now 75p) ... now divide the orange by (1/infinty) each infinitesimally smally partical of the orange = 75p) or the orange is priceless!

whats the value of priceless?
its not number anyway!

[Tristam Green]

Currently, we human don't understand how to divide something by nothing. We just can't wrap our heads around it.

Computers are coded by humans, and so, are generally about as smart as we are. The problem can be solved by using computer AI which evolves and teaches itself, which exists, but is generally used for commercial products, refining a product by evolutionary means to create the "perfect" product, depending on the inserted variables.

So it's possible that something else could figure it out for us. Whether we could understand the results it gives us? Thats another question.


That and, people seem to be afraid of evolving computers. ;)

NO.

The result of x/0 is

DOES NOT EXIST

That is not imaginary, it is not "something we haven't figured out yet", it is an impossibility. Probably the ONLY true impossibility.


dividing by zero is impossible

Thank you, sir.

[Sporkman]

That is not imaginary, it is not "something we haven't figured out yet", it is an impossibility. Probably the ONLY true impossibility.


It is not "impossible", it is simply not applicable for the division operation.

As a previous poster pointed out, you can throw 1/0, 1/(chicken sandwich), 1/(A child's laughter), 1/(that thing I pulled off my toenail), 1/(literacy in the developing world), etc, all into the same "not defined for the division operation" bucket.

[98cwitr]

if you divide any number by 0 you just get infinity. That's it. Any computer can do this, but it will take literally forever no matter how powerful the machine is.

[jrothwell97]

if you divide any number by 0 you just get infinity. That's it. Any computer can do this, but it will take literally forever no matter how powerful the machine is.

No, it won't.

Dividing by zero doesn't equal infinity, although some logic could lead you to believe it does: it's simply undefined, as we've mentioned seemingly an infinite number of times in this thread already. :P

[98cwitr]

No, it won't.

Dividing by zero doesn't equal infinity, although some logic could lead you to believe it does: it's simply undefined, as we've mentioned seemingly an infinite number of times in this thread already. :P

http://www.math.utah.edu/~pa/math/0by0.html

the only problem is that infinity is not a definable number, thus we say dividing by zero is undefined.

[Tristam Green]

No, it won't.

Dividing by zero doesn't equal infinity, although some logic could lead you to believe it does: it's simply undefined, as we've mentioned seemingly an infinite number of times in this thread already. :P

++


http://www.math.utah.edu/~pa/math/0by0.html

the only problem is that infinity is not a definable number, thus we say dividing by zero is undefined.

No. x=infinity = infinity. y=infinity = undefined/impossible.

the two are not the same.

[98cwitr]

++



No. x=infinity = infinity. y=infinity = undefined/impossible.

the two are not the same.

then x=y.

[Tristam Green]

then x=y.

0/0 = impossible by division by zero

[John Bean]

Dividing by zero doesn't equal infinity, although some logic could lead you to believe it does: it's simply undefined, as we've mentioned seemingly an infinite number of times in this thread already. :P

Heh. I haven't read all of them but enough to agree ;-)

I'm not sure why so many people believe the x/0 == infinity fallacy; if it were true you could multiply the result (infinity) by the divisor (zero) giving the original value of x - for any value of x - as happens with non-zero divisors. But since it's not true, you can't.

There, I've just added one to infinity without changing a thing :-)

[MindSz]

Let's say we have 1/4. That means we need to 'break' the numero uno in four equal shares. If you divide by zero, you're breaking this number up in 'no equal shares' ... and if you think about it, that just doesn't make sense.

Even though the limit of 1/x as x approaches 0 is infinity, there's no answer for 1/0. It's not impossible, there's just no answer.

On the other hand, I found this pic in the forums somewhere. I don't know if you've seen it.

[julio_cortez]

I'm not sure why so many people believe the x/0 == infinity fallacy
Well, infinity isn't a number itself.. So you can't really have "infinity" as a result of an operation.
That's why limits have been created I guess, because by using a limit you mean "I'm getting as close as I can, but I'm not exactly there".


There, I've just added one to infinity without changing a thing :-)
There's nothing new to it. Chuck Norris counted to Infinity. Successfully. THREE TIMES.

[John Bean]

That's why limits have been created I guess, because by using a limit you mean "I'm getting as close as I can, but I'm not exactly there".

... and you've still got an infinite distance to go, no matter how close you get :-)

[julio_cortez]

... and you've still got an infinite distance to go, no matter how close you get :-)
Well, when I was a kid I thought that I could have reached infinity before the end of my life if I started counting and never stopped.
I'm now 22353576886544673456435784513424645 and counting. :lolflag:

[Legendary_Bibo]

There's nothing new to it. Chuck Norris counted to Infinity. Successfully. THREE TIMES.

Chuck Norris has nothing on Edward Cullen, oh snap!
In all seriousness, there's got to be more to this though rather than slapping D.N.E. on it. I mean the five main constants in math are pi, e (euler's constant), i (imaginary root), 1, and 0. You'd think there'd be no correlation between let's say e, i, and pi, but I can still recall a crazy equation from Einstein that we had to solve for that involved e^itheta. I don't recall what is was, but it was an assignment by our college professor where it took most people a week to solve. I just have to find my Calc book.
Mathematics is probably by far the purest discipline, but it's not complete just yet.

[John Bean]

Well, when I was a kid I thought that I could have reached infinity before the end of my life if I started counting and never stopped.
I'm now 22353576886544673456435784513424645 and counting. :lolflag:
If your numbers suddenly go negative and start reducing it means you missed the big event. Start again from 1, but with a bit more focus this time :-)

A lot of this sort of stuff comes from bad science fiction rather than bad education I suspect.

[Tristam Green]

Solve the repeating decimal issues first before attempting to divide by zero.

[undecim]

if you divide any number by 0 you just get infinity. That's it. Any computer can do this, but it will take literally forever no matter how powerful the machine is.

No, it's not. If that were the case, the processor would be programmed with a special case for x/0, which returns infinity.

You cannot divide by zero. Period. The most you can do is estimate it by using mathematical limits.

And even then, no one calls it infinity. Instead, we say it has no limit, because, first of all, infinity is a very tricky number (have a look at http://scidiv.bellevuecollege.edu/Math/InfiniteHotel.html if you feel like a mind bender), and second of all, if you are coming from the positive side, the number extends toward positve infinity and coming from the negative side, the number extends toward negative infinity.

Look back at my previous post and you will see that having a number for 1/0 breaks the commutative property of multiplication, which means that 1/0 cannot possibly be a number, because its existence leads to a contradiction

[Sporkman]

first of all, infinity is a very tricky number

Infinity is not a number.

[98cwitr]

No, it's not. If that were the case, the processor would be programmed with a special case for x/0, which returns infinity.

You cannot divide by zero. Period. The most you can do is estimate it by using mathematical limits.

And even then, no one calls it infinity. Instead, we say it has no limit, because, first of all, infinity is a very tricky number (have a look at http://scidiv.bellevuecollege.edu/Math/InfiniteHotel.html if you feel like a mind bender), and second of all, if you are coming from the positive side, the number extends toward positve infinity and coming from the negative side, the number extends toward negative infinity.

Look back at my previous post and you will see that having a number for 1/0 breaks the commutative property of multiplication, which means that 1/0 cannot possibly be a number, because its existence leads to a contradiction

1/0 is not a number, it is infinity.

[RiceMonster]

1/0 is not a number, it is infinity.

How many times do people need to say it isn't ininfity and that it's not possible?

[wojox]

while true; do echo -n "it isn't ininfity and that it's not possible "; done

[del_diablo]

Because the people saying infinity is not computer reachable is doing good ********

[98cwitr]

^^this...roffle


How many times do people need to say it isn't ininfity and that it's not possible?

infinitely many times.

ok fine...its more like 1^-EE where there are an infinite number of zeros between the decimal and the 1.

1^-EE != 0...whatever. Ya'll wanna debate imaginary numbers now too? I'm going to take teh square-root of -1...go.

[RiceMonster]

while true; do echo -n "it isn't ininfity and that it's not possible "; done

8)

[98cwitr]

while true; do echo -n "it isn't ininfity and that it's not possible "; done

Error: No variable defined

[RiceMonster]

Error: No variable defined

Remove the apostrophies.

[doas777]

sure we will. it will be called skynet, and once it's fully online, no one will ask silly questions based on mathematical aberrations of logic, solving the question forever by rendering it moot.

[MarcusW]

Ask and thou shall receive:

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

Still an approximation though (if even that). For 1/x when x -> 0, you still have two different outcomes (+0 and -0), so I'd say it's not even an approximation of (1/0). The solution with imaginary numbers is a bit more straight forward, sqrt(-1) = i.

[Tristam Green]

Because the people saying infinity is not computer reachable is doing good ********

nice; hate and discontent in a MATH DISCUSSION.

:confused::confused::confused:

[McRat]

You don't "reach" a solution for an answer in mathematics, it exists.

While an old school computer or a bad program might go into an infinite loop by trying to solve 1/0, that is a flaw in the algorithm, and has nothing to do with the solution.

To correctly do a reinteritive algorithm for 1/0 you would:

X = 1
Y = 0
R = X

Count = 0

Do while R>=X

R = X - Y
If R=X Then Error
Count = Count +1

Loop

Print "Answer is "; Count
Return Count

:Error

Print"No solution"
Return -1

Or something like that. If you don't check that the Remainder is getting smaller, you have a bad program.

[undecim]

ok fine...its more like 1^-EE where there are an infinite number of zeros between the decimal and the 1.

*I'm going to apologize in advance if this post seems like a flame. I don't mean it to be one, I'm just trying to make a point*

That number would be equal to zero for the same reason that 0.9... (repeating) is equal to one.

And 1/0 is NOTHING like that. It is not infinity, it is not some abstraction that we cannot represent. IT DOES NOT EXIST

Your reasoning is that 1/x gets higher as x approaches 0 from 1, correct?

Then by your reasoning, infinity is equal to negative infinity! If you approach x=0 from -1, then 1/x gets smaller (bigger negative numbers). Punch "y=1/x" into a graphing calculator and look. For that matter, you can approach 0 from any complex number and find that x=1/0 has an uncountably infinite number of solutions ( [infinity]*e^(i[theta]) for 0 <= [theta] < 2[pi] )

Unless you can explain to me how 1/0 can be any one of an uncountably infinite amount of infinite numbers, you cannot say that 1/0 = infinity.

[98cwitr]

You don't "reach" a solution for an answer in mathematics, it exists.

While an old school computer or a bad program might go into an infinite loop by trying to solve 1/0, that is a flaw in the algorithm, and has nothing to do with the solution.

To correctly do a reinteritive algorithm for 1/0 you would:

X = 1
Y = 0
R = X

Count = 0

Do while R>=X

R = X - Y
If R>=X Then Error
Count = Count +1

Loop

Print "Answer is "; Count
Return Count

:Error

Print"No solution"
Return -1

Or something like that. If you don't check that the Remainder is getting smaller, you have a bad program.


looks like an infinite loop where R always =1

[Penguin Guy]

You get infinity.

[98cwitr]

*I'm going to apologize in advance if this post seems like a flame. I don't mean it to be one, I'm just trying to make a point*

That number would be equal to zero for the same reason that 0.9... (repeating) is equal to one.

And 1/0 is NOTHING like that. It is not infinity, it is not some abstraction that we cannot represent. IT DOES NOT EXIST

Your reasoning is that 1/x gets higher as x approaches 0 from 1, correct?

Then by your reasoning, infinity is equal to negative infinity! If you approach x=0 from -1, then 1/x gets smaller (bigger negative numbers). Punch "y=1/x" into a graphing calculator and look. For that matter, you can approach 0 from any complex number and find that x=1/0 has an uncountably infinite number of solutions ( [infinity]*e^(i[theta]) for 0 <= [theta] < 2[pi] )

Unless you can explain to me how 1/0 can be any one of an uncountably infinite amount of infinite numbers, you cannot say that 1/0 = infinity.

no no dude...i was just agreeing with you in my last point...you're right, in 1/x...as x gets closer to 0, y is reaching infinity...but x will never equal 0, but can be infinitely close to 0.


You get infinity. obviously...thus I said "infinite loop."

[lostinxlation]

looks like an infinite loop where R always =1
it jumps to Error label at the 1st attemp.

[solitaire]

Do you think we'll ever have a computer powerful enough to divide by 0?


Maybe....

But knowing what "Quantum super computers" will be like, it will probably give up after a few days become sentient and decide it's eaiser to enslave the human race and see how we like working on improbable math problems 24/7...

[undecim]

no no dude...i was just agreeing with you in my last point...you're right, in 1/x...as x gets closer to 0, y is reaching infinity...but x will never equal 0, but can be infinitely close to 0.

Oh sorry... Misunderstood you.

[98cwitr]

it jumps to Error label at the 1st attemp.

how's that?

[McRat]

looks like an infinite loop where R always =1


Naw, it checks to see if R gets smaller after each subtraction. If R is larger than or equal to X, it's not getting smaller, so you jump out of the loop.

Not intended to be elegant, in the real world you always validate your data before using so you'd just:

If Divisor = 0 then Error.

But that doesn't show that you should ALWAYS determine that a loop will end (unless waiting for input). You should never get into an infinite loop in a program, division or not.

[98cwitr]

oops missed the if statement...ok got it. Seems kinda pointless...like

x=x
if x=x then Error
else Count++
Print Count

[McRat]

oops missed the if statement...ok got it. Seems kinda pointless...like

x=x
if x=x then Error
else Count++
Print Count

Except that it's a really common bug.

If you do not validate your inputs, or check that loops will always complete in a reasonable time, you get nasty bugs. The kind that make you plug the cord from the wall. Stack overflow or buffer overruns often are caused by these.

[Legendary_Bibo]

Except that it's a really common bug.

If you do not validate your inputs, or check that loops will always complete in a reasonable time, you get nasty bugs. The kind that make you plug the cord from the wall. Stack overflow or buffer overruns often are caused by these.

I did one of these in my C++ class, not this one, but I wrote a loop in my program that caused it to do an impossible calculation. I think I got it caught in an infinite loop of trying to divide by zero. It broke the computer :D
Good thing my professor was cool, and told me not to worry about it. He would just tell the staff it was Windows's fault. He was also the one who helped me set up Ubuntu when Vista broke on my laptop. :)

[McRat]

There is another error like it that weird, and that's when you are trying to "intercept" a moving value.

Let's say you want to hit an airplane with a missile, but the airplane's movements are not linear.

You aim at it, then find you are too far left. So you go right. Now you are too far right, etc.

This can have 3 outcomes:

Your guesses get better and better, until you hit.

Your guesses get worse and worse, until you lose contact.

Your guesses are equally bad in both directions, and you go into an infinite loop.

You see this in engine controls, guidance systems etc. Ever have a fuel injected car that "hunts" for it's idle RPM? Then you've seen the last case. It's hard to always spot, and sometimes you there is no "step" value that is correct if the target is moving. You need to identify when it goes into that phase quickly, and use a second type of algorithm to get you past that lump in the data. You may have several different schemes.

Not divide by zero, but something to think about when doing loops. You need to evaluate progress even when the data "looks" like it's making headway.

[PurposeOfReason]

Why is this thread still going on? All I've read since my last post is a lot of people thinking infinity has the same definition of impossible, more who think x/0 = infinity and a few very very bad "proofs" (such as the stupid 1 = (I forget what) which I can find multiple things wrong with; such as division by zero (to keep it itt ;)). Math does not lie, math is one of, if not the most pure science. Yes, some things can just not exist.

Besides the point, if I'm not mistaken this thread has taken a turn to programming (above few posts) which is also making me cringe.

[donkyhotay]

Math does not lie, math is one of, if not the most pure science. Yes, some things can just not exist.

I disagree with your opinion that math doesn't lie, just look at statistics for example. Also math can quite often give results that don't mesh with the "real world" because it requires so many variables or involves things we don't know about or are familiar with. For example many people thought there was a planet closer to the sun then mercury because it's orbit wasn't mathematically correct according to newtonian physics, once relativity came out it was realized that mercury's orbit is correct without having another planet hidden in the glare of the sun.

[Legendary_Bibo]

Why is this thread still going on? All I've read since my last post is a lot of people thinking infinity has the same definition of impossible, more who think x/0 = infinity and a few very very bad "proofs" (such as the stupid 1 = (I forget what) which I can find multiple things wrong with; such as division by zero (to keep it itt ;)). Math does not lie, math is one of, if not the most pure science. Yes, some things can just not exist.

Besides the point, if I'm not mistaken this thread has taken a turn to programming (above few posts) which is also making me cringe.

Programming and math go hand in hand though :)
Yeah I don't get why there's people saying it's infinity either.
Originally I started this before my morning coffee, and at the same time my computer was on which lead to the start of all this. Are super computers just for number crunching? Or can they create, solve, and prove their own mathematical theorems?

[lostinxlation]

Are super computers just for number crunching? Or can they create, solve, and prove their own mathematical theorems?
The scientific applications are about number crunching in most of the parts. If you look back, vector computers were synonymous to super computers till 15 years ago and vector computers were nothing but very powerful SIMD systems which were obviously number crunching systems.
Then they realized designing custom vector units was too costly and found general purpose processors became so powerful that they could make super computers with them. Now they're distributing the operations to many processors instead of vector chaining, but the nature of the applications is the same.

Since today's MPP systems are more of general purpose design, you may be able to solve a mathematical problem, but you need algorithm like any other programs.

[PurposeOfReason]

I disagree with your opinion that math doesn't lie, just look at statistics for example. Also math can quite often give results that don't mesh with the "real world" because it requires so many variables or involves things we don't know about or are familiar with. For example many people thought there was a planet closer to the sun then mercury because it's orbit wasn't mathematically correct according to newtonian physics, once relativity came out it was realized that mercury's orbit is correct without having another planet hidden in the glare of the sun.
Still, IMO that math did not lie there, we just didn't have all the variables. The numbers did just what they should have, it was a human error.

[piousp]

I disagree with your opinion that math doesn't lie, just look at statistics for example. Also math can quite often give results that don't mesh with the "real world" because it requires so many variables or involves things we don't know about or are familiar with. For example many people thought there was a planet closer to the sun then mercury because it's orbit wasn't mathematically correct according to newtonian physics, once relativity came out it was realized that mercury's orbit is correct without having another planet hidden in the glare of the sun.

I disagree. What you mention are NOT proofs that math lie. They may proof that we were using the incorrect theory or just that the theory didnt cover that area in the first place (and thats why they are theories instead of laws). Heck, there is even a Number theory.

[tom66]

A hyperintelligent race just got off the phone to tell me that they've calculated x/0. In order to do it, they created a massive sentient computer called Deep Thought. After 7.5 million years of computation, it turns out x/0 is 42.

[lostinxlation]

A hyperintelligent race just got off the phone to tell me that they've calculated x/0. In order to do it, they created a massive sentient computer called Deep Thought. After 7.5 million years of computation, it turns out x/0 is 42.
Well, Deep Thought lost to Kasparov. Use Deep Blue and answer would be different.

[McRat]

If you throw away mathematics and number theory and think about it, the answer is "What?".

You have a bag of oranges. You want to divide it equally among your 4 siblings, but you find there are 7 oranges, and they will fight over them.

You divide by zero for the solution: You decided to recall the question.

"Hey, what happened to that bag of oranges you had?"

"What?"

[user1397]

what about 0 divided by 0?

[tom66]

0/0 is either 1 or anything, depending on who you ask. If you ask a mathematician, it is 'indeterminate'.

[Legendary_Bibo]

A hyperintelligent race just got off the phone to tell me that they've calculated x/0. In order to do it, they created a massive sentient computer called Deep Thought. After 7.5 million years of computation, it turns out x/0 is 42.

Fascinating, and it all makes sense now, it's the only logical explanation.

[seanelly]

x/0 = e^(infinity)

[Sporkman]

e^(i Pi) + 1 = 0

[undecim]

what about 0 divided by 0?
To elaborate on tom66's answer, it depends on the situation. Sometimes you get 0/0, and can find a value to use from mathematical limits or analysis.

Look at it like this: if 0/0=x, then 0=0*x. In that case, x can be anything.

Here's an example of where you might get 0/0:

y=(x^2 - 4)/(2x^2 + 3x - 2)

if x=-2, what is y? Solving directly, you get 0/0.

But if you get closer and closer to x=-2, from either direction, y approaches 4/5. So in any practical application where you need, you can use 4/5

Or, if you factor both the top and bottom, you'll see

x^2 - 4 = (x+2)(x-2)
2x^2 +3x - 2 = (x+2)(2x-1)

You can cancel the x+2 (which, ironically, is kind of like dividing both terms by zero...) to get y=(x-2)/(2x-1), where for x=-2, y=4/5

[Legendary_Bibo]

To elaborate on tom66's answer, it depends on the situation. Sometimes you get 0/0, and can find a value to use from mathematical limits or analysis.

Look at it like this: if 0/0=x, then 0=0*x. In that case, x can be anything.

Here's an example of where you might get 0/0:

y=(x^2 - 4)/(2x^2 + 3x - 2)

if x=-2, what is y? Solving directly, you get 0/0.

But if you get closer and closer to x=-2, from either direction, y approaches 4/5. So in any practical application where you need, you can use 4/5

Or, if you factor both the top and bottom, you'll see

x^2 - 4 = (x+2)(x-2)
2x^2 +3x - 2 = (x+2)(2x-1)

You can cancel the x+2 (which, ironically, is kind of like dividing both terms by zero...) to get y=(x-2)/(2x-1), where for x=-2, y=4/5

Another way to see this is to use L'ospital's Rule (I know that's not the spelling, but that's how my head remembers it). In which you take the derivative of the numerator and denominator and apply f(a) like so.


lim x^2 - 4 = lim 2x = 4
x-->-2 2x^2+3x - 2 x-->-2 4x+3 5

[tom66]

0/0 is indeterminate because you get tricky questions like the limit of x^2/x (at least that's what I understand... haven't done advanced calculus yet.)

[Legendary_Bibo]

0/0 is indeterminate because you get tricky questions like the limit of x^2/x (at least that's what I understand... haven't done advanced calculus yet.)

sin(x)/x = 1 when x=0

[seanelly]

sin(x)/x = 1 when x=0

Or -1?

[PurposeOfReason]

sin(x)/x = 1 when x=0
http://www.wolframalpha.com/input/?i=sin%280%29%2F0

Try again.

[seanelly]

http://www.wolframalpha.com/input/?i=sin%280%29%2F0

Try again.

What about the limit of sin(x)/x as x -->0? Or like I mentioned earlier with the numerator and denominator's limits approaching from opposite sides.

ie - (lim_(x->0) (sin(x)) / x)

[PurposeOfReason]

What about the limit of sin(x)/x as x -->0? Or like I mentioned earlier with the numerator and denominator's limits approaching from opposite sides.
Taking a limit is just that, it is the limit as you approach a value, it is not the value itself. As stated, sin(0)/0 is still division by zero and thus undefined. Taking the limit does not change that.

[Legendary_Bibo]

http://www.wolframalpha.com/input/?i=sin%280%29%2F0

Try again.

limit notation is a pain in the *** on these forums, but if I must



lim sin(x) = 1
x-->0 x


Oh and try plugging that into a calculator. Remember, computers don't understand the concept of limits.

[PurposeOfReason]

limit notation is a pain in the *** on these forums, but if I must



lim sin(x) = 1
x-->0 x
Oh and try plugging that into a calculator. Remember, computers don't understand the concept of limits.
Read the above post. You could always latex it up and post that here, that way you're not talking about two different things. Still doesn't change what I said.

[Legendary_Bibo]

Taking a limit is just that, it is the limit as you approach a value, it is not the value itself. As stated, sin(0)/0 is still division by zero and thus undefined. Taking the limit does not change that.

sin(x)/x is one of those exceptions though because L'ohpitale's Rule states it's actually 1. Allow me to demonstrate.



lim sin(x) = lim cos(x) = 1
x-->0 x x-->0 1

[PurposeOfReason]

sin(x)/x is one of those exceptions though because L'ohpitale's Rule states it's actually 1. Allow me to demonstrate.



lim sin(x) = lim cos(x) = 1
x-->0 x x-->0 1

I remember calculus, it was way more fun to forget than it was to learn.

[MasterNetra]

You would think it be simple, i mean 85 / 0 is 0 sense there is nothing at all to go into 85 to begin with, so nothing will come out of it.

[seanelly]

You would think it be simple, i mean 85 / 0 is 0 sense there is nothing at all to go into 85 to begin with, so nothing will come out of it.

You have 85 to begin with.

[lisati]

A hyperintelligent race just got off the phone to tell me that they've calculated x/0. In order to do it, they created a massive sentient computer called Deep Thought. After 7.5 million years of computation, it turns out x/0 is 42.
Even the forums have an error #42. I've had it appear a couple of times in the last three years when asking vBulletin to do the imposisble.

[Legendary_Bibo]

I remember calculus, it was way more fun to forget than it was to learn.

Really? I have fun learning it, and all sorts of mathematical concepts. The philosophy of math is so interesting. :D

[MasterNetra]

You have 85 to begin with.

Isn't the output suppose to represent how many times the following number after the first, goes into the first number? Or is the output suppose be the number after modification if the latter I think we have developed Division incorrectly.

While I can of course preform the operations, Whats going on with the numbers, their exact roles in the operations and what happens to them has been quite hazy when it comes to multiplication and division. It has yet to be explained to me in a way that is clear. And I seem to have difficulty working with it because I don't understand fully what is going on with the operation, which causes trouble for me in higher math as you might imagine.

[PurposeOfReason]

Really? I have fun learning it, and all sorts of mathematical concepts. The philosophy of math is so interesting. :D
Not saying it isn't. I can still take the flux integral in spherical coordinates if you need me to, but ask me to remember all the stupid rules that you need one in every thousand+ times, no thanks.

[seanelly]

Taking a limit is just that, it is the limit as you approach a value, it is not the value itself. As stated, sin(0)/0 is still division by zero and thus undefined. Taking the limit does not change that.

I say it's close enough - I bet you aren't an engineer. :P 1 is also the more interesting answer.

[Legendary_Bibo]

You would think it be simple, i mean 85 / 0 is 0 sense there is nothing at all to go into 85 to begin with, so nothing will come out of it.

wait, what? Now reverse it. Does 0 * 0 = 85?
I say we develop a constant to represent division by zero. I vote for the letter strauss for being a representation of that constant.

[Legendary_Bibo]

Not saying it isn't. I can still take the flux integral in spherical coordinates if you need me to, but ask me to remember all the stupid rules that you need one in every thousand+ times, no thanks.

I can state the LaGrange error bound formula off the top of my head, but yours sounds more interesting.

[MasterNetra]

wait, what? Now reverse it. Does 0 * 0 = 85?
I say we develop a constant to represent division by zero. I vote for the letter strauss for being a representation of that constant.

I am saying that 0 isn't a value but a placeholder for absolute nothing and shouldn't even exist in a equation except to represent the value of nothing, but it should not be processed other then as a removal of the values prior to its result. I'd imagine the Greeks thought zero had no place in equations too, which why they never used 0. I mean if there is nothing, why even have it in the equation to begin with. It just seems illogical. Zero is fine when displaying as a final result, eg. 25-25=0 as it shows that nothing is left, but to process it in multiplication, and divison... I mean any zero results within the process should be counted as removal, Though I am not aware of such a thing happening in multiplication or division without starting with zero, which should be a no-no to begin with, but none the less.

[Shining Arcanine]

Still an approximation though (if even that). For 1/x when x -> 0, you still have two different outcomes (+0 and -0), so I'd say it's not even an approximation of (1/0). The solution with imaginary numbers is a bit more straight forward, sqrt(-1) = i.

I never thought I would need to use one of these, but that response takes the cake:

http://i472.photobucket.com/albums/rr82/Raven8401/picard_facepalm.jpg

There is no such thing as positive or negative when dealing with zero. It is neither positive or negative nor even or odd.

By the way, remove any association you have between limits laws and the concept of approximation from your head. The entire idea behind them is that when something is taken to the limit, it is perfect.

[seanelly]

I am saying that 0 isn't a value but a placeholder for absolute nothing and shouldn't even exist in a equation. I'd imagine the Greeks thought this too, which why they never used 0. I mean if there is nothing, why even have it in the equation to begin with. It just seems illogical. Zero is fine when displaying as a final result, eg. 25-25=0 as it shows that nothing is left, but to process it in multiplication, and divison... I mean any zero results within the process should be counted as removal, Though I am not aware of such a thing happening in multiplication or division without starting with zero, which should be a no-no to begin with, but none the less.

You and zero need to go for beers. You can thank zero for a lot of luxuries you take for granted. Without zero, many gadget, machines, and systems that you use would be horridly unoptimized. :P

[MasterNetra]

You and zero need to go for beers. You can thank zero for a lot of luxuries you take for granted. Without zero, many gadget, machines, and systems that you use would be horridly unoptimized. :P

Not if the appropriate adjustments to the processes where made. I am not dismissing zero from math completely, I just think its being misused in the multiplication/Division arena. I mean come on. The computer can't even processes a value / zero. Clearly we are doing something wrong. Though as a amendment I should clarify that I don't support its use in Multiplication/Division Operations.

[Legendary_Bibo]

I never thought I would need to use one of these, but that response takes the cake:



There is no such thing as positive or negative when dealing with zero. It is neither positive or negative nor even or odd.

By the way, remove any association you have between limits laws and the concept of approximation from your head. The entire idea behind them is that when something is taken to the limit, it is perfect.

I think he's referring to right and left limits though which...wait now I feel dumb that's just a test for continuity.

[undecim]

I am saying that 0 isn't a value but a placeholder for absolute nothing and shouldn't even exist in a equation except to represent the value of nothing, but it should not be processed other then as a removal of the values prior to its result. I'd imagine the Greeks thought zero had no place in equations too, which why they never used 0. I mean if there is nothing, why even have it in the equation to begin with. It just seems illogical. Zero is fine when displaying as a final result, eg. 25-25=0 as it shows that nothing is left, but to process it in multiplication, and divison... I mean any zero results within the process should be counted as removal, Though I am not aware of such a thing happening in multiplication or division without starting with zero, which should be a no-no to begin with, but none the less.

0 is a value. Just like -1 is a value. Negatives aren't palceholders at all, but actual mathematical values. It has it's proper place in equations.

For example, cos(0) = 1, or x^0 = 1

[MasterNetra]

0 is a value. Just like -1 is a value. Negatives aren't palceholders at all, but actual mathematical values. It has it's proper place in equations.

For example, cos(0) = 1, or x^0 = 1

Zero represents nothing, and thus cannot be a true value other then the representation of nothing in a expression. Why the heck are people trying to treat nothing as something? Such illogic.

Also what x^0 tells me is nothing was done to x, remember the default value given to the variable is 1. so x^0 = 1^0, so really when you look at it, nothing was done to begin with, and what cos(0) = 1 tells me is that cos = 1, again nothing was done to cos. Which apparently must equal 1 to begin with.

[Legendary_Bibo]

Zero represents nothing, and thus cannot be a true value other then the representation of nothing in a expression. Why the heck are people trying to treat nothing as something? Such illogic.
0 is a natural NUMBER. It is a number, an origin point so to speak within any dimension.

[MasterNetra]

0 is a natural NUMBER. It is a number, an origin point so to speak within any dimension.

Again, 0 represents nothing as a number, it is still a place holder. By nature what we call numbers are just symbols that are suppose to represent a value or in zero's case the lack there of. And again I am not dismissing the value of nothing completely from math.

[McRat]

Zero is the origin.

It is as critical to math, geometry, physics, business as the concept of numbers themselves.

It is not a null value. It is not "nothing".

You can't even make the simplest shapes without at least a relative zero. A circle is the simplest shape, and it's defined as the set of points with the same distance from origin. It can always be defined as a radius and an offset from zero. 3 digits.

[lisati]

Ever noticed that "nothing" is something whose meaning we can define in terms of what it's not, i.e. no + thing?

[MasterNetra]

Zero is the origin.

It is as critical to math, geometry, physics, business as the concept of numbers themselves.

It is not a null value. It is not "nothing".

You can't even make the simplest shapes without at least a relative zero. A circle is the simplest shape, and it's defined as the set of points with the same distance from origin. It can always be defined as a radius and an offset from zero. 3 digits.

That doesn't mean it has a actual quantity to it. Besides Geometry != Multiplication and Division. But even in geometry 0 has no quantity value. But point of origin needs none apparently to represent a center of something (which when it comes down to it is a different use of the symbol 0 then what is used for general math).
(Unfortunately I do seem to substitute terms at times, though the fact I was originally speaking about multiplication and division should of made it obvious i was referring to 0 having no value as far as Quantity. I mean with multiplication/Division what other type of value would there be?)

[undecim]

Zero represents nothing, and thus cannot be a true value other then the representation of nothing in a expression. Why the heck are people trying to treat nothing as something? Such illogic.

Also what x^0 tells me is nothing was done to x, remember the default value given to the variable is 1. so x^0 = 1^0, so really when you look at it, nothing was done to begin with, and what cos(0) = 1 tells me is that cos = 1, again nothing was done to cos. Which apparently must equal 1 to begin with.

Zero does not represent nothing. In math, there is a symbol to represent nothing, and that is Ø, which means null.

x^0 doesn't mean that nothing was done to x. No matter what x is, x^0=1 (except where x=0, because that's the same thing as dividing by 0) 2^0=1, 3^0=1, pi^0=1.

Also, I don't think you understand cosine. Cosine is a function, which means you put one thing into it, and another thing comes out. In the case of cos(0), that is the notation for saying that we give the function cosine the number 0, and it gives us the number 1. cos by itself is just a funciton, not a number

[MasterNetra]

Zero does not represent nothing. In math, there is a symbol to represent nothing, and that is Ø, which means null.

x^0 doesn't mean that nothing was done to x. No matter what x is, x^0=1 (except where x=0, because that's the same thing as dividing by 0) 2^0=1, 3^0=1, pi^0=1.

Also, I don't think you understand cosine. Cosine is a function, which means you put one thing into it, and another thing comes out. In the case of cos(0), that is the notation for saying that we give the function cosine the number 0, and it gives us the number 1. cos by itself is just a funciton, not a number

Well then what Quantity value does 0 represent? If it doesn't represent nothing/lack of quantity then what does it represent? Then is it really correct to say that when you have no carrots that the number of carrots in your possession is 0? Because that would suggest that 0 represents nothing/lack of quantity (Which in quantity cases lack of quantity=nothing).

Also I was taught that the default value of x (or any variable) in a math expression (if a value is not given anyway) is one. So if x=1 in cases where no x value is given, and if no x value was given. (Which was so in this case) then in x^0=1 the ^0 part of the expression must actually do nothing as x=1 and the result was in deed 1. Unless the statement of course you provided was incorrect.

As for cosine, indeed i have forgotten what exactly it didn't but i must wonder in cos(0)=1 how was it that the function arrived at one without any quantity value stated? Or does 0=1? Or some higher number broken down into one, or perhaps a decimal number brought up to 1?

[undecim]

Well then what Quantity value does 0 represent? If it doesn't represent nothing/lack of quantity then what does it represent? Then is it really correct to say that when you have no carrots that the number of carrots in your possession is 0? Because that would suggest that 0 represents nothing.

It does represent nothing, but 0 itself is not nothing (as contradictory as that sounds)

Let me give you a practical application to explain it. If you want to have a number to describe the stock in the produce section of the grocery store. The manager will have a number for carrots, apples, and grapes. If the store runs out of apples, then the number for apples is 0, and if you ask someone who works in that are, they will say "we have no [0] apples"

But if you ask that same person how many bottles of cola they have, they will say "We don't have cola in this department." They don't have a number for cola in the produce section. If you need a symbol to represent that, you would use Ø. Even though they don't have any apples either, they still keep track of what number they have.

[lisati]

Well then what Quantity value does 0 represent? If it doesn't represent nothing/lack of quantity then what does it represent? Then is it really correct to say that when you have no carrots that the number of carrots in your possession is 0? Because that would suggest that 0 represents nothing.

I think I see what's happening here. Apologies if my explanation is a bit disjointed: some of the discussions so far have been related to stuff I had long forgotten, and Mrs Lisati is expecting me to give attention to a discussion of domestic duties and responsibilites.

The thing about numbers is that sometimes they represent quantities of tangible objects, such as when we're counting stuff like carrots. Other times, they are useful when representing intangible stuff, abstractions if you like, such as measurements of size.

(I might come back and elaborate a little bit if Mrs Lisati lets me!)

[MasterNetra]

It does represent nothing, but 0 itself is not nothing (as contradictory as that sounds)

Let me give you a practical application to explain it. If you want to have a number to describe the stock in the produce section of the grocery store. The manager will have a number for carrots, apples, and grapes. If the store runs out of apples, then the number for apples is 0, and if you ask someone who works in that are, they will say "we have no [0] apples"

But if you ask that same person how many bottles of cola they have, they will say "We don't have cola in this department." They don't have a number for cola in the produce section. If you need a symbol to represent that, you would use Ø. Even though they don't have any apples either, they still keep track of what number they have.

The explanation still supports the notion that 0 represents nothing. In fact you admitted it does. I already figured the use of 0 was kept track for display the absence of something, but it still does not figure in as a actual quantity value. It just shows that the lack there of, and unless your showing that something that there was no quantity and quantity was then added, or debt was created (in the case of negative numbers). It seems rather illogical to do much else with it from a quantity perspective.

Edit: And the power cord to my laptop (which is my main computer) died, computer sometime afterwards, glad i kept my old gateway desktop...)

[Legendary_Bibo]

That doesn't mean it has a actual quantity to it. Besides Geometry != Multiplication and Division. But even in geometry 0 has no quantity value. But point of origin needs none apparently to represent a center of something (which when it comes down to it is a different use of the symbol 0 then what is used for general math).
(Unfortunately I do seem to substitute terms at times, though the fact I was originally speaking about multiplication and division should of made it obvious i was referring to 0 having no value as far as Quantity. I mean with multiplication/Division what other type of value would there be?)

it has a quantitative value of nothing...

[undecim]

The explanation still supports the notion that 0 represents nothing. In fact you admitted it does. I already figured the use of 0 was kept track for display the absence of something, but it still does not figure in as a actual quantity value. It just shows that the lack there of, and unless your showing that something that there was no quantity and quantity was then added, or debt was created (in the case of negative numbers). It seems rather illogical to do much else with it from a quantity perspective.

In a way, 0 does represent nothing. It represents a quantity of nothing, but a quantity of nothing is still a quantity.

Think of it like a measurement. If you measure the distance between two points and find the distance to be 0, then you can still use 0 to represent that measurement. The measurement is not nothing.

[MasterNetra]

In a way, 0 does represent nothing. It represents a quantity of nothing, but a quantity of nothing is still nothing.

Think of it like a measurement. If you measure the distance between two points and find the distance to be 0, then you can still use 0 to represent that measurement. The measurement is not nothing.

Then your agreeing with me, as this does not conflict with what I just said. In fact it supports.

[Legendary_Bibo]

Then your agreeing with me, as this does not conflict with what I just said. In fact it supports.

No no no no, this goes back to vector quantities and scalar quantities. 0 as a vector quantity means nothing. A scalar value of 0 means a measurement of a value of nothing.

[undecim]

Then your agreeing with me, as this does not conflict with what I just said. In fact it supports.

Actually, that wasn't what I meant to say (bad writing on my part, but I fixed it, so reread my post)

My point is that you have to have something to say that a measurement has nothing to it. You still made that measurement and still have a number to go with it, and that number is 0.

[MasterNetra]

No no no no, this goes back to vector quantities and scalar quantities. 0 as a vector quantity means nothing. A scalar value of 0 means a measurement of a value of nothing.

In either case the there really isn't a difference. Again 0 is showing nothing at all. But my original point was with multiplication/division anyway. If you must, then why would 5 x 0 = 0? should not 5 x 0 = 5 sense 0 isn't (or shouldn't) actually do anything I mean how do you go to having a value, attempting to multiply and end up with no value. I mean with 0 its not even multipling itself and should remain the same. it should be 5 x 0 = 5 = 5 (by itself). As for that whole able to switch the numbers from either end of the multiplication sign, that's do-able when you have two actual quanties involved, but 0, it represents the lack there of. So fact not being able to that with it, should not be so surprising. 0 x 5 = 0 however is understandable as under normal cirmstances your not able to get something from nothing.

As for divison 5 / 0 should also be 5. As nothing is technically being done to 5. The checks. simple sense nothing is actually being done, drop the zero to right of a value. 5 x 0 = 5, drop 0 and your left with 5. same with divison. in more complex multiplication 5 x 0 x 6 = 30 = 5 x 6, zero really just shouldn't be there.

[undecim]

In either case the there really isn't a difference. Again 0 is showing nothing at all. But my original point was with multiplication/division anyway. If you must, then why would 5 x 0 = 0? should not 5 x 0 = 5 sense 0 isn't (or shouldn't) actually do anything I mean how do you go to having a value, attempting to multiply and end up with no value. I mean with 0 its not even multipling itself and should remain the same. it should be 5 x 0 = 5 = 5 (by itself). As for that whole able to switch the numbers from either end of the multiplication sign, that's do-able when you have two actual quanties involved, but 0, it represents the lack there of. So fact not being able to that with it, should not be so surprising.

Showing 0 is NOT showing nothing at all. It is showing a quantity. That quantity represents nothing, BUT IT IS STILL A QUANTITY. It is still a measurement and still a number and is still subject to all the same properties that other numbers are, with some exceptions (such as division by 0)

And when you use that quantity in an operation with another quantity, you will get a result. That's why 5 x 0 = 0. If it were just nothing, we couldn't use it in multiplication and couldn't get it as a result.

I think you REALLY need to figure out the difference between a quantity and what that quantity represents. 0 is a quantity, not what it represents. 0 is something. We can add it, subtract it, multiply by it, divide it by things, use it as an input to functions, and define statements equal to it all day long.

[MasterNetra]

Showing 0 is NOT showing nothing at all. It is showing a quantity. That quantity represents nothing, BUT IT IS STILL A QUANTITY. It is still a measurement and still a number and is still subject to all the same properties that other numbers are, with some exceptions (such as division by 0)

And when you use that quantity in an operation with another quantity, you will get a result. That's why 5 x 0 = 0. If it were just nothing, we couldn't use it in multiplication and couldn't get it as a result.

I think you REALLY need to figure out the difference between a quantity and what that quantity represents. 0 is a quantity, not what it represents. 0 is something. We can add it, subtract it, multiply by it, divide it by things, use it as an input to functions, and define statements equal to it all day long.

There is no visable logic to what you are saying. Adding 0 to 5 results to 5, thus (to me at least) indicating that it doesn't really do anything to actual quantity values. And thus to me indicating that all 0 is really (when dealing with quantity) just a placeholder for nothing (no quantity) and as such manlipulating actual values is not plausable. (with zero) you of course can add value, but thats not a manlipulation from 0's end. Saying 0 represents nothing but yet is something (other then a symbol representing nothing) is a conderdiction. Unless of course it also represents something else that does have a value, Which case this addtional representation(s) have not been made known to me. Well ok other then it being a point of orgin. Which still does nothing to actual quantity values. It gives a point of reference, nothing more.

[jrothwell97]

There is no visable logic to what you are saying. Adding 0 to 5 results to 5, thus (to me at least) indicating that it doesn't really do anything to actual quantity values. And thus to me indicating that all 0 is really (when dealing with quantity) just a placeholder for nothing (no quantity) and as such manlipulating actual values is not plausable. (with zero) you of course can add value, but thats not a manlipulation from 0's end. Saying 0 represents nothing but yet is something (other then a symbol representing nothing) is a conderdiction. Unless of course it also represents something else that does have a value, Which case this addtional representation(s) have not been made known to me. Well ok other then it being a point of orgin. Which still does nothing to actual quantity values. It gives a point of reference, nothing more.

You're not making sense here.

x * 0 = 0 is a defined identity in the mathematical world, just like x + x = 2x or x * x = x^2.

There is a difference between 0 and nothing. 0 is a defined quantity of nothing: generally, when you use zero on its own, you mean "zero units" (although we rarely bother mentioning units, since it's practically a given.)

Zero can mean "no nuts," "no litres of water," "no CDs." Five times zero is simply "no lots of 5" - hence, it is also zero.

Dividing something by zero, on the other hand, is undefined. There is no agreed identity as to what dividing by zero will actually give you, in the same way there's no definition as to what the blankwart (represented, in my mathematical lexicon, by the ☺ symbol) of a number is.

So, for the final time,

x / 0 ≠ 0
x / 0 ≠ ∞
x / 0 ≠ anything!

[McRat]

It could be argued that Zero is the only honest number, the rest are proxies.

If I have a unit, I have 1.
If I split it into two parts, what do I have?

Well, if it's base10, you have 0.5
If it's hex, you have 0.8
If it's octal, you have 0.4
If it's binary? You have 0.1

Wait. 5,8,4,1 are ALL just 1/2?? Only Zero is sincere.
:guitar:

[Tristam Green]

yeesh. the "my math skillz are better than urs" is making my eyes bleed.

[halovivek]

Zero "0" is nothing.
Nothing cannot be divided by nothing.
Because nothing has no value. if you divide you should get a value on that. Since zero itself non-value with a value (zero) for our reference. It is impossible to do with zero.

[samh785]

A number is a mathematical object, an abstract object which does not exist at any particular time or place. Is something like this real? :)
How do you know anything is real? All you can possibly know for certain (without making assumptions) is that you can think.

[Hyporeal]

This discussion reminds me of a certain counting system with only three numbers: "one", "two", and "many". This system is like our counting numbers except "many" stands for all numbers greater than two. The problem is to find x = many - two. The forum discussion on whether x exists would parallel this one, with some insisting that x can't exist while others speculate on whether x = many, one, two, or some yet unimagined number. It strikes me that the whole debate is artificial, based on self-imposed restrictions.

[Sporkman]

How do you know anything is real? All you can possibly know for certain (without making assumptions) is that you can think.

Descartes pondered that. He came to the conclusion that the only thing he could be certain of is that he exists (based on the fact that he can think about the problem as you mentioned).

That is the basis of the erroneous quote "I think therefore I am".

[donkyhotay]

Descartes pondered that. He came to the conclusion that the only thing he could be certain of is that he exists (based on the fact that he can think about the problem as you mentioned).

That is the basis of the erroneous quote "I think therefore I am".

Always wondered about that, I mean it seems obvious enough but it assumes that you are thinking, and it also assumes something must exist in order to think. What if either of these aren't true? What if you aren't actually thinking (but somehow stating this), or that you can think without actually existing? Admittedly I can't wrap my head around either of these ideas to make sense but I have wondered about it.

[Sporkman]

Always wondered about that, I mean it seems obvious enough but it assumes that you are thinking, and it also assumes something must exist in order to think. What if either of these aren't true? What if you aren't actually thinking (but somehow stating this), or that you can think without actually existing? Admittedly I can't wrap my head around either of these ideas to make sense but I have wondered about it.

It depends on how you define "exist" I suppose. One definition would be if an entity can "do" something (like think about itself), then it must at the very least "exist". Descartes said that as far as anything else goes, such as what he sees, touches, feels, etc, he could be deceived about.

[RiceMonster]

How do you know anything is real? All you can possibly know for certain (without making assumptions) is that you can think.

Because senses are not required to confirm everything. I do not need senses to know 1 + 1 = 2. Yes, numbers DO exist because they are simply words to describe a concept.

[MasterNetra]

Because senses are not required to confirm everything. I do not need senses to know 1 + 1 = 2. Yes, numbers DO exist because they are simply words to describe a concept.

But you needed the senses to learn it. Otherwise without our senses we would not even know there is a environment around us. Or even know what material is. In fact without senses we would be void of even consciousness, as really consciousness = awareness, to be aware you need at least a form of sensory.

[John Bean]

really consciousness = awareness, to be aware you need at least a form of sensory.

So you think that self-awareness is not actually real?

My brain hurts... or maybe it doesn't ;-)

[MasterNetra]

So you think that self-awareness is not actually real?

My brain hurts... or maybe it doesn't ;-)

Without any form of sensory, you wouldn't be aware at all. Self-Awareness still utilizes sensory. You receive pain because of what we often referred to as touch receptors (not their scientific name, but it works), little nerves that stretch all throughout your body and report touch related activities including that which we refer to as pain back to the brain which then interprets the signals accordingly. Without them. Pain would be unknown to us. In fact all touch related activities would not be "felt" at all.

[John Bean]

I disagree, let's leave it at that.

Oh... and the brain doesn't have any pain sensors, so when I said "my brain hurts" it had nothing to do with sensory perception.

[sydbat]

I disagree, let's leave it at that.

Oh... and the brain doesn't have any pain sensors, so when I said "my brain hurts" it had nothing to do with sensory perception.Remember that scene in Scanners...?

[MasterNetra]

I disagree, let's leave it at that.

Oh... and the brain doesn't have any pain sensors, so when I said "my brain hurts" it had nothing to do with sensory perception.

Perhaps not, but apparently there is around the brain, the scalp, and bone. You cannot feel pain where there are no receptors. It just not do-able with how the human body works. If you think you feel it where there are none, then your clearly mistaken about its location.

[John Bean]

Remember that scene in Scanners...?

Indeed. Definitely nothing to do with sensory perception, quite the reverse in fact :-)

[John Bean]

Perhaps not, but apparently there is around the brain, the scalp, and bone. You cannot feel pain where there are no receptors. It just not do-able with how the human body works.

Then why does my brain hurt?

No need to answer that because:

1. you can't possibly know the answer, and
2. it was a rhetorical question, and
3. I think you may be suffering from irony deficiency ;-)

[MasterNetra]

Indeed. Definitely nothing to do with sensory perception, quite the reverse in fact :-)

Scifi shows don't count. Their pieces of fiction, and usable for evidence as to how things work.

[ibuclaw]

Erm... anyone heard of nan? Many programming languages handle it.

x / 0 = nan.

Solved. :)



OK, joke aside. If you really want to know why division by 0 is impossible to resolve. See http://home.ubalt.edu/ntsbarsh/zero/zero.htm

[MasterNetra]

Then why does my brain hurt?

No need to answer that because:

1. you can't possibly know the answer, and
2. it was a rhetorical question, and
3. I think you may be suffering from irony deficiency ;-)

1. I am aware of the fact that in order to feel anything a signal needs to be sent to the part(s) of the brain that interprets and processes that. While granted misfires or activity within the body can trigger touch/pain receptors.

Also again their are pain receptors in a covering around the brain (and bones) referred to as the "meninges". It is from somewhere (if not multiple locations) from this layer that the signals are being sent from. Not from the inners of the brain itself.

If the whole thing seems to hurt it seems more the likely the brain is being expanded (e.g. blood vessels within the brain have expanded) and it pressing against the outer covering.)

Or wait I just remembered blood vessels themselves are suppose to have pain receptors, it can be from them too that signals are sent.

Here is some support: http://en.wikipedia.org/wiki/Pain

Yes I know wiki can be incorrect in some if not multiple cases, but really any documentation produced could be.

[MasterNetra]

Erm... anyone heard of nan? Many programming languages handle it.

x / 0 = nan.

Solved. :)



OK, joke aside. If you really want to know why division by 0 is impossible to resolve. See http://home.ubalt.edu/ntsbarsh/zero/zero.htm

"... If one does allow oneself dividing by zero, then one ends up in a hell. That is all. ..."

lol

[undecim]

There is no visable logic to what you are saying. Adding 0 to 5 results to 5, thus (to me at least) indicating that it doesn't really do anything to actual quantity values. And thus to me indicating that all 0 is really (when dealing with quantity) just a placeholder for nothing (no quantity) and as such manlipulating actual values is not plausable. (with zero) you of course can add value, but thats not a manlipulation from 0's end. Saying 0 represents nothing but yet is something (other then a symbol representing nothing) is a conderdiction. Unless of course it also represents something else that does have a value, Which case this addtional representation(s) have not been made known to me. Well ok other then it being a point of orgin. Which still does nothing to actual quantity values. It gives a point of reference, nothing more.

I'm afraid you sorely misunderstand what mathematical operations do...

In math, things don't happen, they simply exist.

For example, in the equation 2+4=6, the 4 isn't doing anything to the 2 and the 2 isn't doing anything to the 4. The numbers don't become 6. Instead, we are simply using those symbols to say "the sum of 2 and 4 is 6".

This is handy, because instead of using numbers, we can use anything that represents a quantity, such as x or (x+2) or even (x^y-(wx/4)). That is why we can say "The sum of 2 and 0 is 2", because 0 represents a quantity or nothing.

Lets say that we have the equation a+1. I'm sure you will agree that variables represent quantities and can be used in equations just as numbers are. Now we say a=0. This is saying "a represents the same quantity as 0". a still represents a quantity and you can still use operations on it, even though it represents 0.

If you can't understand that, then there is no more to discuss here. I'm guessing that you haven't had much math education, but one day you will be taught by someone you will believe (i.e. a teacher) that 0 is just as much a number as any other.

[MasterNetra]

I'm afraid you sorely misunderstand what mathematical operations do...

In math, things don't happen, they simply exist.

For example, in the equation 2+4=6, the 4 isn't doing anything to the 2 and the 2 isn't doing anything to the 4. The numbers don't become 6. Instead, we are simply using those symbols to say "the sum of 2 and 4 is 6".

This is handy, because instead of using numbers, we can use anything that represents a quantity, such as x or (x+2) or even (x^y-(wx/4)). That is why we can say "The sum of 2 and 0 is 2", because 0 represents a quantity or nothing.

Lets say that we have the equation a+1. I'm sure you will agree that variables represent quantities and can be used in equations just as numbers are. Now we say a=0. This is saying "a represents the same quantity as 0". a still represents a quantity and you can still use operations on it, even though it represents 0.

If you can't understand that, then there is no more to discuss here. I'm guessing that you haven't had much math education, but one day you will be taught by someone you will believe (i.e. a teacher) that 0 is just as much a number as any other.

I've had plenty, but all that was taught was the how to solve portion. Never really the why its that way, or the idea behind the equation's formation or anything like that. And when I did ask about such things, they clearly didn't know the answers to what I wanted to know then.

And I just can't accept nothing as a quantity, for me quantity involves substance, and 0 represents the lack there of, and the notion nothing is something makes no sense to me as I see it as a complete contradiction. But I suppose unless I figure out a math system that can be used just as well if not better then whats current then I suppose its a moot point.
At any rate the education system (at least here in the US) spends too much time focusing on teaching how to solve equations and not enough on understanding it.

[jerenept]

you all hurt my head. 2/0=????????

That is all.

[Austin25]

They covered that in Calculus, but I drank those brain cells away many years ago. It's not infinity, nor zero.

It seems many CPU/MPU's? have look-up tables for division, so it justs reports an error.

Remember when the first batch of Pentiums had an error in the look-up tables and got some math problems wrong? I still have one of the keychain Pentiums from that release somewhere.
why is it not infinity?

[MasterNetra]

you all hurt my head. 2/0=????????

That is all.

Yes, let that be all. We don't need math. Just peanut butter.

[lostinxlation]

why is it not infinity?
Because there is no such a number called infinity. You can use infinity as '-> infinity', but usingit as '= infinity' doesn't make sense.


Regarding the handling of division by 0 on computers, some architectures treat it as an exception. I don't know about x86, but SPARC has division_by_zero exception and it immediately takes a trap when it is detected and the trap handlers will most probably terminate the program.

[Austin25]

Because there is no such a number called infinity. You can use infinity as '-> infinity', but usingit as '= infinity' doesn't make sense.
10/10 = 1
10/9 = 1.11...
10/8 = 5/4 =1.24
10/8 = 1.4285...
10/6 = 5/3 = 1.66...
10/5 = 2
10/4 = 5/2 = 2.5
10/3 =3.33...
10/2 =5
10/1 =10
10/.5 =20
10/.25 =50
10/0 =infinity?

[lostinxlation]

10/10 = 1
10/9 = 1.11...
10/8 = 5/4 =1.24
10/8 = 1.4285...
10/6 = 5/3 = 1.66...
10/5 = 2
10/4 = 5/2 = 2.5
10/3 =3.33...
10/2 =5
10/1 =10
10/.5 =20
10/.25 =50
10/0 =infinity?
Not sure what your point is, but what do you think about this, then ?

10/0 = infinity
10/(infinity*0) = 1
infinity*0 = 10 ?

Infinity is not a specific number, so that you cannot involve it in a simple arithmetic operation.

[PC_load_letter]

No, 5 = -5. I proved it. In the universe bounded by this thread, division by zero is defined and 5 = -5.

Well, if this is what you want, here is a shorter 'proof' ;)

For any real numbers a, b,: a.0 = 0 = b.0
Dividing both sides by zero, we get: a = b

[papangul]

An understanding of the eastern concept of dualism is the key for anyone to understand the real fundamental problem behind this topic.( and it might be difficult for the uninitiated western mind to comprehend that)

Wikipedia Link (http://en.wikipedia.org/wiki/Dualism#In_Eastern_mysticism)

dualism can mean the tendency of humans to perceive and understand the world as being divided into two overarching categories

all opposites are manifestations of the single Tao, and are therefore not independent from one another, but rather a variation of the same unifying force throughout all of nature.

In the East, the dualistic worldview is considered to be the realm of ordinary mind and in order to get in touch with the real reality, one is expected to transcend the ordinary mind to reach a higher, "no-mind" (http://en.wikipedia.org/wiki/Mushin) state of being. The ordinary mind functions mechanically out of preconceived ideas and preset assumptions. The "no-mind" or the "mind of no-mind" is a state of heightened awareness, where intuition, rather than just mechanical reaction is called into play.

In Zen(the "haiku" people) koans (http://en.wikipedia.org/wiki/Koan) were used as a tool to break out from the shackles of ordinary mind. Basically, these are nonsensical statements that would kill the mind(head) of the person who approached to solve them mentally(ie. by logical thinking) and shock him into awareness.

koan is a question, or statement; the meaning of which cannot be understood by rational thinking
eg. of koan: sound of one hand clapping.


What I am trying to say is:

1. 0 & 1 are the building block of computers, but they are the products of a limited dualistic worldview.

2. The problem of dividing by zero is a koan.

So, as far I get it, dividing by zero has nothing to do with computational power. It is something that is beyond the domain of computers.

[seanelly]

You cannot divide by zero and you cannot have a number equal to infinity. While this similarity is not proof that x/0 = infinity, if we remember that infinity is just a concept, I don't see the harm in assuming that it's true. I'm content to go through life with my belief that x/0 = (+/-)infinity and until I see a irrefutable proof convincing me otherwise, well... some people have Jesus and I have this. :P

[lisati]

Because there is no such a number called infinity. You can use infinity as '-> infinity', but usingit as '= infinity' doesn't make sense.


Regarding the handling of division by 0 on computers, some architectures treat it as an exception. I don't know about x86, but SPARC has division_by_zero exception and it immediately takes a trap when it is detected and the trap handlers will most probably terminate the program.

I see "infinity" more as an abstraction than an actual number that you would use in, say, figuring out the ingredients of a good cup of coffee, representing instead something like humongous (http://www.worldwidewords.org/weirdwords/ww-hum2.htm), and then some.

If memory serves correctly, the x86 line generates an int0 for a divide-by-zero exception. [citation needed]

[alexfish]

An understanding of the eastern concept of dualism is the key for anyone to understand the real fundamental problem behind this topic.( and it might be difficult for the uninitiated western mind to comprehend that)



2. The problem of dividing by zero is a koan.

So, as far I get it, dividing by zero has nothing to do with computational power. It is something that is beyond the domain of computers.

That the Whole Point of the Question

Is'nt IT as in IT

[corney91]

This thread makes me sad :(
All the maths to prove that infinity is not a number, or solution to a equation, and division by zero is not just hard to do, it's impossible. If you can't get you're head round it, I'd advise giving up - there a incomprehendable things in this world and this problem can be one of them, depending on how your brain works :)

sin(x)/x is one of those exceptions though because L'ohpitale's Rule states it's actually 1. Allow me to demonstrate.



lim sin(x) = lim cos(x) = 1
x-->0 x x-->0 1

You can also use the Maclaurin series of sin to prove this if I remember correctly... :)
EDIT: just looked up the series expansion and it divides by zero so never mind :p


And I just can't accept nothing as a quantity, for me quantity involves substance,
What about negative numbers? Or complex numbers?

[Shining Arcanine]

I think he's referring to right and left limits though which...wait now I feel dumb that's just a test for continuity.

That is precisely why I posted the picard face palm.


Again, 0 represents nothing as a number, it is still a place holder. By nature what we call numbers are just symbols that are suppose to represent a value or in zero's case the lack there of. And again I am not dismissing the value of nothing completely from math.

There is a difference between nithil and zero. Remember, nihil is a noun and zero is an adjective. Some languages such as Latin lack a way of expressing quantities of zero, because there is no adjective to describe it.

[John Bean]

"Zero" is a noun.

[Shining Arcanine]

"Zero" is a noun.

While they have functions as nouns (particularly when referencing them), numbers are adjectives like colors and tastes while the things they modify are nouns like dogs. If they were nouns and not adjectives, you could substitute any other noun in place of one in a sentence and still have a grammatically correct sentence. i.e. If numbers were nouns "Five cats" would become "Dogs cats", which is not grammatically correct, however, since numbers are adjectives "Five cats" could become "Red cats" or "Sour cats", which are both grammatically correct.

[donkyhotay]

While they have functions as nouns (particularly when referencing them), numbers are adjectives like colors and tastes while the things they modify are nouns like dogs. If they were nouns and not adjectives, you could substitute any other noun in place of one in a sentence and still have a grammatically correct sentence. i.e. If numbers were nouns "Five cats" would become "Dogs cats", which is not grammatically correct, however, since numbers are adjectives "Five cats" could become "Red cats" or "Sour cats", which are both grammatically correct.

And by extension of course zero as a number is also an adjective as in "zero cats" which I believe is your point though you didn't directly state it.

[yossell]

There are coherent mathematically well defined number systems that do incorporate infinity. See, for instance, http://en.wikipedia.org/wiki/Extended_real_number_line and there's also a coherent arithmetic of transfinite numbers: http://en.wikipedia.org/wiki/Transfinite_number

However, the rules for these number systems are rather different from the rules that govern the integers, the rationals and the reals, and the physical significance of these numbers is debatable.

[Legendary_Bibo]

It's interesting to see where this discussion has led, and I've looked at several math proofs, and they just prove why division by zero isn't infinity. They however don't prove what it is though. I call for a new constant.

[Shining Arcanine]

It's interesting to see where this discussion has led, and I've looked at several math proofs, and they just prove why division by zero isn't infinity. They however don't prove what it is though. I call for a new constant.

The most you can do is take limit as the denominator approaches zero, which produces infinity. If you want to represent that by a constant, then call it infinity. That is what infinity means anyway.

[StephenF]

The most you can do is take limit as the denominator approaches zero, which produces infinity. If you want to represent that by a constant, then call it infinity. That is what infinity means anyway.
There are two limits. If you take the negative one it produces -infinity.

[JKyleOKC]

It's interesting to see where this discussion has led, and I've looked at several math proofs, and they just prove why division by zero isn't infinity. They however don't prove what it is though. I call for a new constant.That'll be fine, once you find a number that when multiplied by zero gives a result of 6; that number will be the quotient for 6/0. You'll actually need an unlimited number of such constants, though: one for each integer! (I prefer to say "unlimited" rather than "infinite" although both words have the same meaning.)

[Legendary_Bibo]

That'll be fine, once you find a number that when multiplied by zero gives a result of 6; that number will be the quotient for 6/0. You'll actually need an unlimited number of such constants, though: one for each integer! (I prefer to say "unlimited" rather than "infinite" although both words have the same meaning.)
Xi with a supscript that implies what's being divided by zero.

[luceerose]

The problem is the presence of 0 itself within the mathematical system.
0 is just a placeholder used to describe a complete lack of something tangible that was expected in it's stead.
A "null", so to speak, to describe a lack of something that just didn't show up.
"Nothing" is used to describe a lack of something that DOES exist. Therefore Nothing CANNOT exist or be defined without first defining the "something". In this manner Nothing|Null|0 is required in computer programing, etc, to define a place to go when "something" expected simply didn't happen.
In mathematics the "somethings" are positive integers, the presence of which is always implied & never questioned.
In real world physics, though, "nothing" simply DOES NOT EXIST anywhere in the universe. There is nowhere in Quantum Mechanics|Atomic/Sub-Atomic Theory that you will find an object that can be defined as being completely non-existent.
Even in what could be regarded as a perfect vacuum there still exists time &/or space which, by all accounts, is still considered to be comprised of "something".
To simplify on the Physics front; you can say that an atom contains 0 electrons, but that simply means those electrons are off somewhere else in the universe. Not non-existent.

For all intensive purposes 0 simply describes a state of the non-existence of all other numbers & is only used in regular mathematics to describe special circumstances.
Zero should therefore not be regarded as a number unto itself, or at least not to the point where we are inventing theoretical paradoxes to extrapolate something beyond it's limited usefulness.

[lisati]

Ah, the joys of coming up with a practical definition of what we're talking about!

[papangul]

@larsenguitars: Hats off to you for debunking zero (or our understanding of it). But your explanation increased my skepticism about all numbers. :confused:

If zero cannot exist without defining "something" first, can any number exist on it's own, independently, without an accompanying substance (or "something" that the number is used to measure in some way) being defined first? I say "1 apple", "2 oranges" etc. Do they("1" or "2") mean anything when they are separated from the apples and oranges and made to stand on their own?


Therefore Nothing CANNOT exist or be defined without first defining the "something".

That is not much different from what MasterNetra had said earlier in the thread (he used the word "substance" instead of "something"):
And I just can't accept nothing as a quantity, for me quantity involves substance, and 0 represents the lack there of...

Look here at what numinous said in response to MasterNetra's statement:
This is an odd statement.
Numbers are real objects but they aren't substances.
They have properties particular to each number and our mind understands these properties through symbols.
Zero is just another number. It is useful in the measurement of physical quantities, but it's real apart from these as a mathematical object.

He is claiming all numbers including zero are real objects and have their independent existences.

[Tristam Green]

Know why you cannot assign a value to f(x) = x/0?


Because you cannot define that which is undefined.

[handy]

I find it so hard to understand that this thread has lasted so long? :confused:

[YuiDaoren]

I find it so hard to understand that this thread has lasted so long? :confused:
http://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

[red_Marvin]

If numbers can only be motivated by their ties to tangible objects I expect an escalation in the conflict when somebody introduces negative numbers.

There is a difference between math and 'counting things I can see'.

[mmix]

There is a difference between math and 'counting things I can see'.

Also there is a difference between assembly and 'cpu instructions I can see'.

[Windows Nerd]

For the lolz (http://www.thinkgeek.com/images/products/thumb/largesquare/de50_in_russia.jpg)

[Jeff12518]

It is not that division by zero is impossible. To divide by zero means that no action has been taken, therefore there is no result. No question was asked so no answer can be given.

[Legendary_Bibo]

Ξ6 = 6/0

[doas777]

in Soviet Russia, zero divides by you, effectively solving this debate.

of course it started another argument about how each individual would be enumerated. the question has been held up in committe for the last 40 years or so.

[98cwitr]

if we can have imaginary numbers then I think we should bullsh*t our way into dividing by zero.

[donkyhotay]

maybe thats the question to the ultimate answer!

x/0=42

j/k (c:

[Ender985]

This thread is amazing. Reminds me the recurrent threads at Blizzard forums where 0.99999_ != 1

But for all of you that are well past that, all the people that are not scared by let's say " e^(pi*i) = -1 "; I hereby present you with yet another nonsensical mathematical demonstration of 1 = -1 :


1 = √1 = √[(-1)*(-1)] = √(-1)*√(-1) = i*i = -1 tadaaa!

[MindSz]

You can't actually do this
1 = √1 unless you're only in N. If you want to take negatives into account, you need to solve the quadratic
√x = 1and this has two solutions: 1 and -1.

[sisco311]

lol

[Странник]

The answer is 42

[limestone]

from now on i decide that anything divided with 0 = 2 :)
suck it!!

[corney91]

if we can have imaginary numbers then I think we should bullsh*t our way into dividing by zero.

No, imaginary numbers were discovered, not made up - and the reciprocal of zero doesn't exist so it can't be discovered ;)

[Legendary_Bibo]

I had to tutor someone today, and their math book was horrible. It had one example about limits that made me think of this thread :D
That's right I think of you guys ;)


lim 1 = infinity
x-->0 x
Sorry if it looks funky. We need to be able to add formulas for these types of discussions :)

For one thing it didn't even explain why it was infinity, which I thought we just listed it as Does Not Exist.

[98cwitr]

I had to tutor someone today, and their math book was horrible. It had one example about limits that made me think of this thread :D
That's right I think of you guys ;)


lim 1 = infinity
x-->0 x
Sorry if it looks funky. We need to be able to add formulas for these types of discussions :)

For one thing it didn't even explain why it was infinity, which I thought we just listed it as Does Not Exist.

you do know what lim means right?

As x approaches 0, it doesn't and never will equal 0. Now grab your trusty calculator and divide 1 b y .1 and see what you get and then do it again for .01, and so on until you get the point.

[98cwitr]

No, imaginary numbers were discovered, not made up - and the reciprocal of zero doesn't exist so it can't be discovered ;)

discovered = made up?

[new_tolinux]

For one thing it didn't even explain why it was infinity, which I thought we just listed it as Does Not Exist.
It should not be infinity.

As it's simple maths that x/x=1

Besides that I still think about what they teach on primary school: dividing or multiplying by zero equals zero.
As my teachers always stated during my schooltime: dividing by zero is an exception to the basic x/x=1 rule and the x*y=z therefore z/x=y and z/y=x rules because zero isn't a value, zero is nothing.

So unless they're wrong (which wouldn't surprise me at all :lolflag:) it seems that this is a non-existing question.

[alphaniner]

If zero is nothing and not a value, then why does x^0 equal 1?