Dividing by zero

Originally posted by yampa
Black holes were produced as a theoretical speculation *first* - they were not trying to explain unexplained data. If the original speculation is false, and you can point out mathematically why it is false then why would you return to a broken theory?

I watched this a while ago when you first posted it and cant be bothered to watch it again so I can't deconstruct any particular point that he made. However I will still make a few points from memory...

Black holes were concieved by laplace and some other guy I cant remember by simply calculating the mass / radius required to have an escape velocity of C. Nothing is wrong with this. It is simply a rearrangement of the Newtonian escape velocity calculation.

Einstein was well aware that GR fell over when describing the interior of black holes. GR is probably incorrect in these circumstances but that doesnt mean black holes can't exist

Originally posted by tremex
That means there are infinitely many solutions to the equation 0/0 =x.

Infinitely many solutions?

A bright kid from junior high would point out the fact that

a/a = 1

It follows that if a=0, then

a/a = 0/0 = 1

and therefore there is a unique solution to equation 0/0 = x, with the solution being x=1. Since 0 = 0*1, the multiplication check holds.

Zero is not infinity. Infinity can be infinitesimally small or infinitesimally large. Zero is not in the set of anything with substance, it is nothing.... nill..... the absence of anything..... you cannot give it a sign. it is undefined.

You can play a lot of games with it, but it is, and always will be, nothing.

Originally posted by charlyv
Zero is not infinity. Infinity can be infinitesimally small or infinitesimally large. Zero is not in the set of anything with substance, it is nothing.... nill..... the absence of anything..... you cannot give it a sign. it is undefined.

You can play a lot of games with it, but it is, and always will be, nothing.

Does 0 elephants weigh more than 0 squirrels?

Since 0 = 0, then the absence of elephants weighs the same as the absence of squirrels. It follows that the volume of nothing in the lunch box equals the volume of nothing in the space between galaxies.

reply to post by Moduli


A bit off topic but something ive been dying to know, and you seem like you know a bit of physics; Has there ever been created a legit animation of what the most knowledgeable physicists know photons look like? More specifically a photon being created from an accelerated electron? I would love to see them put their math where their eyes are, and create a pseudo physical animation of what their math tells them reality is.

Originally posted by tremex


Since 0 = 0, then the absence of elephants weighs the same as the absence of squirrels. It follows that the volume of nothing in the lunch box equals the volume of nothing in the space between galaxies.

Thats not true. Because space does not = nothing. And volume implies area, which implies real distance between points. Whiche implies that the distance between the sun and earth, is less then the distance between the sun and a star in another galaxy...or were you joking?

You can't divide by zero. That is not technically dividing.

I like how after so many posts, so many people are still no closer to having any understanding of this property of basic grade-school arithmetic.

Originally posted by ImaFungi
A bit off topic but something ive been dying to know, and you seem like you know a bit of physics; Has there ever been created a legit animation of what the most knowledgeable physicists know photons look like?

Well, a photon doesn't really "look like" anything. The "look" of something is, of course, not really a well-defined concept for something you can't really see. The pictures you see are just cartoons that illustrate some properties of it that are easy to draw (e.g., the electric and magnetic fields as perpendicular sine waves). A more sophisticated "picture" is that a photon is really a thing which behaves as if it is a point-particle when measured to be at a particular location, but is otherwise an extended "wave-like" cloud, which describes what the electromagnetic field looks like. Although the "pictures" are less useful than just understanding the math, so you don't really see too many cartoons of these kinds of things, since they are at best not as useful as understanding, and at worst, misleading.

There isn't really a "picture" for what a particle emitting a photon looks like either. The particle emission is described in terms of there having been, quantum mechanically, the possibility of a state which contained the emitted particle in addition to the other particles. This state existed before the emission happened, and was a part of the total state of the system, but was included with a very small probability. After the emission, it is included with a probability nearly equal to one. This process has a very precise description in terms of quantum field theory. But there isn't really a good picture you can draw for it.

Originally posted by tremex

Originally posted by charlyv
Zero is not infinity. Infinity can be infinitesimally small or infinitesimally large. Zero is not in the set of anything with substance, it is nothing.... nill..... the absence of anything..... you cannot give it a sign. it is undefined.

You can play a lot of games with it, but it is, and always will be, nothing.

Does 0 elephants weigh more than 0 squirrels?

Since 0 = 0, then the absence of elephants weighs the same as the absence of squirrels. It follows that the volume of nothing in the lunch box equals the volume of nothing in the space between galaxies.

No, it does not. There is no such thing as a volume of nothing, so there is nothing you could measure it against. In fact, 0=0 does not make any mathematical sense as well, since you cannot compare undefined to anything, even itself.

I just used a Google calculator and divided 6/0 and the answer was 0...

Also, when I calculated the 0 squared, the answer was 1...

Furthermore, the answer for the square root of 0 is 0...

From those answers and the insight I got from the posted video on the subject on page one, I concluded that the Google calculator is being naughty!

Well, at least I arrived at some conclusion...

Originally posted by ilian51378
I just used a Google calculator and divided 6/0 and the answer was 0...

Also, when I calculated the 0 squared, the answer was 1...

Furthermore, the answer for the square root of 0 is 0...

From those answers and the insight I got from the posted video on the subject on page one, I concluded that the Google calculator is being naughty!

Well, at least I arrived at some conclusion...

edit on 4/9/13 by ilian51378 because: (no reason given)

edit on 4/9/13 by ilian51378 because: (no reason given)

It is because the programmer obviously had to trap the resultant error, which is an illegal operation, producing a NAN (not a number) and decided to just display '0', instead of an error message. Otherwise, crashing the script. Boo on them for not letting the user know why.

Originally posted by charlyv
It is because the programmer obviously had to trap the resultant error

Hey at least that programmer trapped the error, unlike the programmer for the US Navy who didn't trap the error and the ship's propulsion shut down as a result.

Division by zero

On September 21, 1997, a division by zero error on board the USS Yorktown (CG-48) Remote Data Base Manager brought down all the machines on the network, causing the ship's propulsion system to fail.

Perhaps the programmer could have just trapped the error and told the program to skip that value and go on to the next one, and the ship wouldn't have shut down.

Also while people are correct in saying division by zero is undefined, it is defined as in exception in the IEEE floating point standard:

The IEEE floating-point standard, supported by almost all modern floating-point units, specifies that every floating point arithmetic operation, including division by zero, has a well-defined result. The standard supports signed zero, as well as infinity and NaN (not a number). There are two zeroes, +0 (positive zero) and −0 (negative zero) and this removes any ambiguity when dividing. In IEEE 754 arithmetic, a ÷ +0 is positive infinity when a is positive, negative infinity when a is negative, and NaN when a = ±0. The infinity signs change when dividing by −0 instead.

As this graph shows you approach positive and negative infinity from dividing by smaller positive and negative numbers, so having a single zero won't work, which is why they define a positive zero and a negative zero (and you thought they were the same, right? They are I suppose, but not in floating point exception handling).

Originally posted by charlyv

Originally posted by tremex

Originally posted by charlyv
Zero is not infinity. Infinity can be infinitesimally small or infinitesimally large. Zero is not in the set of anything with substance, it is nothing.... nill..... the absence of anything..... you cannot give it a sign. it is undefined.

You can play a lot of games with it, but it is, and always will be, nothing.

Does 0 elephants weigh more than 0 squirrels?

Since 0 = 0, then the absence of elephants weighs the same as the absence of squirrels. It follows that the volume of nothing in the lunch box equals the volume of nothing in the space between galaxies.

No, it does not. There is no such thing as a volume of nothing, so there is nothing you could measure it against. In fact, 0=0 does not make any mathematical sense as well, since you cannot compare undefined to anything, even itself.

0=0 doesn't make any mathematical sense?

Number zero is well defined - it is a real number
mathforum.org...
and therefore the identity 0=0 holds like it is with any case a=a where a is a real number.

The expression a/0 is undefined, not number zero itself. You mixed it up. If number zero was undefined, then numbers like 10, 20, 30, ... or any number containing zero wouldn't make any sense. (And so it wouldn't any event that took place in this year 2013 including your post. )

Originally posted by charlyv

Originally posted by ilian51378
I just used a Google calculator and divided 6/0 and the answer was 0...

Also, when I calculated the 0 squared, the answer was 1...

Furthermore, the answer for the square root of 0 is 0...

From those answers and the insight I got from the posted video on the subject on page one, I concluded that the Google calculator is being naughty!

Well, at least I arrived at some conclusion...

edit on 4/9/13 by ilian51378 because: (no reason given)

edit on 4/9/13 by ilian51378 because: (no reason given)

It is because the programmer obviously had to trap the resultant error, which is an illegal operation, producing a NAN (not a number) and decided to just display '0', instead of an error message. Otherwise, crashing the script. Boo on them for not letting the user know why.

The word illegal made me feel like one could be arrested for doing it... haha

Originally posted by tremex

Originally posted by tremex
That means there are infinitely many solutions to the equation 0/0 =x.

Infinitely many solutions?

A bright kid from junior high would point out the fact that

a/a = 1

It follows that if a=0, then

a/a = 0/0 = 1

and therefore there is a unique solution to equation 0/0 = x, with the solution being x=1. Since 0 = 0*1, the multiplication check holds.

No a bright kid from junior high would be in an algebra class and learn that 0/0 is undefined because you have to divide by 0. It won't be until he enters high school and takes Calculus and learns that the limit of x/x where x->0 is 1. This isn't the same thing as saying 0/0 = 1 though.

By the way the math doesn't work, because you can also so that 0/0 = 2 and the multiplication of both sides by 0 will still work out. In fact you could put any number complex, real, imaginary, whole, etc as the answer to the problem 0/0 = x. The multiplication check would still work. Heck you could even throw complex equations as the answer to that problem and the multiplication check would still work. 0/0 = sin^2(x) + 2x^3 - e^x? Sure why not? Just multiply both sides by 0. Hence the value of 0/0 is undefined.

Of course this doesn't even get into the fact that in order to cancel out the 0 divisor on the left you have to calculate 0/0. In other words you have 0 * (0/0) = 0 * x

Originally posted by Krazysh0t
By the way the math doesn't work, because you can also so that 0/0 = 2 and the multiplication of both sides by 0 will still work out. In fact you could put any number complex, real, imaginary, whole, etc as the answer to the problem 0/0 = x. The multiplication check would still work. Heck you could even throw complex equations as the answer to that problem and the multiplication check would still work. 0/0 = sin^2(x) + 2x^3 - e^x? Sure why not? Just multiply both sides by 0. Hence the value of 0/0 is undefined.

That's close but not exactly why. The expression 0/0 is called an "indeterminable case" with the following consequence that ends in contradiction. Consider this transitive case:

If (0/0 = 1) and (0/0 = 2) then 1 = 2.

That's what mathematicians hate to see.

But there is a convention that puts both cases a/0, where a is different from zero, and 0/0 into one box labeled "undefined." There is really no point in making the distinction between "undefined" and "indeterminable." Once you enter zero into the denominator, your computation ends right there one way or the other, unless you are in some really esoteric branch of math.

reply to post by Moduli


Thats quite a shame. My view is that if something exists and occurs, and is some type of something, a form, in some type of space, it has to have qualities that could be expressed in any number of forms, graphing, animation, step by step picture, after all reality really expresses the existence of electrons creating photons in an animated event, if physiscts know how this occurs mathematically, and are confident they comprehend what occurs physically and realistically, I dont see why they couldnt work with talented animators and simulators to recreate what the universe does, just so us laymen can further comprehend and understand how reality occurs.

I was of the impression that electrons didnt project stored potential photons from within them, out into the surrounding space, but that electrons were in some way coupled to the "em/photon field", and when an electron is accelerated or its direction altered, this creates what we understand as photons, or em radiation.

It could be said simple:

What if you have 4 cookies, and you divide it between 0 people, how many cookies does each person get? Its not infinite, but neither its 0 or any real number. You are basically dividing those cookies towards infinity, but common sense says it can't be infinite, that would mean your 4 cookies are actually infinite cookies, only then it would make sense (infinite divided by infinite should be 0)

Time index 4:30, Kaku says: "Here is the problem: When r is equal to zero. The point at which physics itself breaks down".

Because blackholes are real...does this mean that our model of how we calculate and perceive things is wrong?

When some smart dude will find the correct model of calculating all things, will a blackhole be no "mystery" anymore and will it fit nicely into all other calculations?

I mean, what we call a singularity isn't really something weird....we always did approach it the wrong way...Now the math won't be breaking down anymore?

While I am at it...that is maybe the reason why we always did think that something travelling faster than the speed of light is impossible..

I do not know that very much about physics and math but...I am just saying..