I might have just disproved math.

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No, because only Chuck Norris can divide by Zero

Keal:
Hi Zack,

If you really want to understand the problems in your example, you have to start at rather basic mathematics: the notion of a Group.
A Group is a set G together with an operation such that the following axioms hold:

Closure:
If a and b are elements in G the ab is also in G.

Associativity:
For a,b,c in G the equality a(bc)= (ab)c holds.

Neutral element:
There is an element e in G such that ae =ea = a for all a in G. e is called the neutral or the unit element.

Inverse element:
For every a in G there is a b in G such that ab = ba = e. b is called the inverse of a and is formally denoted by a^(-1).

If we have Commutativity (a,b in G: ab = ba), we speak of an abelian Group.

From these axioms you can derive the "rules of calculus" you are used to from school (for the abstract group G).

If you look closely you will see that this group structure is realized in the real numbers R, even in two different ways.

First: the real numbers and addition (R,+)
Closure and associativity are trivial, the neutral element is 0 and the inverse of an element a is (-a). Note that the "-" is more a way to denote the inverse rather then an operation it self.

Second: the real numbers without zero and multiplication (R\{0},*)
Closure and associativity are trivial again, the neutral element is 1 and the inverse is 1/a. Again division is not an operation but a way to denote the inverse and that is reason way "it is forbidden to divide by zero", there is no multiplicative inverse of zero in the real numbers, i.e. there is no a in R such that a*0=1.
So if you decide "to do it anyway" you loose the group structure and the "rules of calculus" you derived using this structure do not apply anymore. That is why it seems easy to construct paradoxes starting from "1/0".

For completeness: If you "combine" two abelian groups with a distributive rule (a,b,c in G (a+b)c= ac+bc) you get a field. If you do that for (R,+) and (R\{0},*) you get the "normal" real numbers with addition and multiplication.

Seems logical, but I have a (probably stupid/obvious) question. When working with the field of "normal" real numbers, I have often (I think?) multiplied by 0. for example in the quadratic x^2=0, the solutions are both zero. This is apparently a thing you would do using the "rules of calculus" (I think, anyway). If you are never allowed to use the number 0 in the "normal" real numbers, How come I seem to come across it so much in my "normal" maths lessons? Can you explain, please?

Hopefully I haven't made too many idiotic statements.

Zack1501:

gumba killer:
You can't divide by zero.

Why not?

To quote the Terminator in T2, "It doesn't work that way."

Seriously though. What many people don't realize is that the "rules of mathematics" are actually completely arbitrary and have no relation whatsoever to the "real world".

All concepts in Mathematics are idealized abstractions and have nothing to do with the "real world" other than maybe being inspired by their "real world analog". The reason maths is useful at all is because many things in the real world approximate or correctly maps to some of the abstract mathematical concepts being studied - if they do great, or they don't too bad.

The rules of mathematics (a.k.a. axioms) are for most part completely "made up". They are most of the time chosen because they are "interesting" to the mathematician and occasionally because it's useful.**

**However they do have to be "consistent", meaning they must not contradict one another.

Keal:
So if you decide "to do it anyway" you loose the group structure and the "rules of calculus" you derived using this structure do not apply anymore.

I think that's going a bit too far.
Yes, if you "do it anyway" you lose the group structure, due to the definition of what a group is, but that doesn't mean you have to loose all the "rules of calculus", you just have to be careful with them, and adapt them occasionally.

asacatman:
Seems logical, but I have a (probably stupid/obvious) question. When working with the field of "normal" real numbers, I have often (I think?) multiplied by 0. for example in the quadratic x^2=0, the solutions are both zero. This is apparently a thing you would do using the "rules of calculus" (I think, anyway). If you are never allowed to use the number 0 in the "normal" real numbers, How come I seem to come across it so much in my "normal" maths lessons? Can you explain, please?

Hopefully I haven't made too many idiotic statements.

Put simply, it's because fields have been built to account for that. So they allow it.

One reason it's okay, is because you can do multiplication by 0 using the addition of the field instead of the multiplication.
a*0 = a + (-a) for all a in the field.

Sexy Devil:

Zack1501:

Sexy Devil:

Punch 0/0 into your calculator for me and see what happens. Nothing divides by 0, not even 0. Full stop. The end.

Ok, I get it I'm wrong(If you people actual paid closer attention to my post you would realize i didn't think it was true ether) But this answer pissed me off the most. You punch something into your calculator and it said error so you ignore it? You don't care why? Just because a calculator cant understand it does not mean thats the end.

I do know why it's wrong, for starters. But any decent calculator will tell you exactly why 0/0 is wrong by stating "Undefined."

But yeah, if you can't trust your calculator with basic algebra then you might want to look into getting a new one.

A bad calculator will say "error"
A good calculator will just go "Divide by Zero"
A better calculator will say "Undefined"
But Amazing calculator will say that it is, in fact, "Indeterminate" or undetermined. If you really think about, though it has its many flaws, theres something interesting behind this pointless math. I didn't think I could determine what mathematicians around the world could not but thats a sorry reason not to try.

Your point is not idiotic at all, indeed I was a bit unclear about that.
I did not mean to abolish zero, we need it to make the addition work and it is a perfectly good number as you pointed out. But although it does not fit in group structure of the multiplication it is still true that a*0=0 for all a in R.
This property makes multiplying by zero to solve an equation rather useless, because you loose all the information (the result is always 0=0 and the the starting equation and 0=0 are not considered equivalent).

Zack1501:

Okysho:

Zack1501:

I wanted to know zero divided by zero equals. I tried to do at algebraically. This is what I did:

-The answer I was trying to get will be represented by x
0/0=x
-I times both sides by zero
0=0x

I've only got a few seconds but here's your first mistake. You can't do this. It's bad math. When you multiply both sides by zero, it's not just "moving one digit from one side to the other" you're creating an x/x situation (which equals 1) 0/0 is undefinded therefore by your equation in this multiplication step:

0/0=x
0(0)/0 = 0(x)
but you're still left with a 0/0 it cannot divide out to make 1.

Here's what you're doing without using 0.

x/7 = y
7(x)/7 = y(7)
x = y(7)

See the error?

This is not the error. It is not 0(0)/0 it is 0(0/0) and as we all know anything times 0 equals 0 so the entire side is 0 thus 0=x0. The error is me saying x=0 when x does not, it just can equal 0.

You still can't do that mathematical operation. Again, the beginning of your proof is based on the simple mathematical principal of "moving from one side to the other" which is in fact creating an x/x = 1 situation.

What you've just told me still doesn't hold up though. 0(0/0) won't evaluate to 0=x(0) (for one thing 0/0 is undefined, but let's roll with it) you'll wind up with 0=x, therefore 0=0 and still doesn't disprove that x/0 is undefined (as in indeterminate) ...

Oddly enough, (contrary to what the great Yahtzee says) Alice in wonderland is a book about how silly mathematics is.

Maze1125:
snip

Keal:
snip

Thanks, you answered my question, even if I didn't totally understand the answer. (mostly through this being a topic I'm a bit ignorant about, despite doing some elementary group theory.)

FalloutJack:
That part was actually a joke, the imaginery VS real bit. However, I'm going to need some citation on the part of you stating that imaginery numbers have an application beyond thought experiment. Since 'i' is literally representing a paradox, and that this is actually the tamest aspect of math acting less like science and more like philosophy, it smacks of carelessness. "We didn't feel like figuring out where this leftover piece of the puzzle actually comes from, so here, have a Lowercase-I."

As has been mentioned before, i is not a paradox - the letter is a representation of a number that, when squared, is equal to -1. The thing about i is it does not lie on the real number line (hence the term "imaginary"), because it is not a member of the set of real numbers (pretty much by definition, because any real number times itself cannot be less than 0).

But the set of complex numbers, of which i is a member, does not take the form of a line - it's a plane, and because of this fact, the complex numbers have certain properties that the real numbers don't. For example, every root of every complex number is itself a complex number. (For real numbers, this is only true for roots of positive numbers and even roots of negative numbers - all other roots of negative numbers are complex numbers, of which the real numbers are a subset.)

The mathematics of the complex plane give rise to a special identity, e^(i*pi)+1=0, aka Euler's Identity. One of the consequences of this identity is that using complex numbers greatly simplifies the analysis and design of digital signal filters.

To say nothing of the quaternions, a higher-dimension analog of the complex plane in which -1 has three square roots, labeled i, j, and k. One notable use of quaternions is as a representation of camera rotations and orientations in 3D games that allows for freely-rotating cameras that are immune to Gimbal Lock.

In short, just because you can't personally see applications for a given bit of math, doesn't mean those applications don't exist.

thewaever:
Everyone who says "you cannot divide by 0" has never taken calculus.

Zack1501:
So, I have an interesting math based question. If you don't like/hate math or don't understand basic algebra(I understand if you don't) just hit the big THE ESCAPIST logo in the corner ...snip... 0/0 also then x=0
-If you fallowed so far and remember that x can be any number then that means zero can also be any and every number. So 0 can now equal 5 or any other number.

I realize something is most likely wrong here.
So tell me escapist, Did i Disprove math?

None of your math is incorrect, but your conclusion is slightly off.

What you are doing here is better dealt with with calculus than algebra, but the short version is this:

First, you are correct in saying that 0 divided by 0 MIGHT equal a number.

Calculus shows that 0 divided by 0 has four possible answers.
Those answers are 0, 1, undefined, or infinity.

It all depends on what the actual value of 0 is.

So, no, you did not disprove math. What you actually did was discover some very developed mathematical ideas.

i dont mean to be a party pooper, but this is wrong. 0 plays a role in the methods of calculus, but before calculus was even discovered the definition of 0, and all its interesting properties, had been solidified and accepted. see thread here on the escapist titled

Dividing by zero, the truth (this is long!)

No. You didn't. It's like trying to disprove the fact that you have ten fingers by repeatedly counting them and every time you get 10 you say you made a mistake and have another go.

image

no you did not and cannot disprove math. At best you found a fallacy and even then its probably a known fallacy.

Multiplying both sides of the equation by zero is eqivalent to wiping the equation off the blackboard. It makes the value of both sides of the equation zero for sure, but in the process it destroys any meaning the equation might have had.

At the end of the day, all you've 'proved' is that zero equals zero.

Zack1501:
So, I have an interesting math based question. If you don't like/hate math or don't understand basic algebra(I understand if you don't) just hit the big THE ESCAPIST logo in the corner and that will bring you home.

I wanted to know zero divided by zero equals. I tried to do at algebraically. This is what I did:

-The answer I was trying to get will be represented by x
0/0=x
-I Multiply both sides by zero
0=0x
-This equals out to be 0=0 because anything times 0 is 0.
-This proves that x can be any number. for example if 5=x than 0=5*0 still is 0=0
-I rearrange 0=0x to be:
0/x=0
-Now since x can be any number now lets say x=0
-That makes this:
0/0=0
-And since x=0/0 (Right in the beginning^) and 0=0/0 also then x=0
-If you fallowed so far and remember that x can be any number then that means zero can also be any and every number. So 0 can now equal 5 or any other number.

I realize something is most likely wrong here.
So tell me escapist, Did i Disprove math?
Edit: I see the error now. Its not that x equals 0 its that at one point x CAN = 0

...ninja'd by OP himself. The larger point I'd make is that Zero always = nothing. It's representative of something that doesn't exist; it's a unique, even singular, number.

Is this now 6 pages of people saying "you can't divide by 0"?

Zack1501:

gumba killer:
You can't divide by zero.

Why not?

Oh God. If there was any doubts by anyone that you knew math, this just verified them.

This is a basic rule of math. Go back to Elementary school.

I figured this was going to be stupid the moment I read the title of this thread, and now I have been proven correct. Unlike your math.

Hal10k:

z121231211:
Because obviously mathematicians haven't thought of this idea before you did.

Hey, that's an incomplete sentence. I think you've just disproved the English language.

OT: I think you need to rethink this problem.

z121231211:
Because obviously mathematicians haven't thought of this idea before you did.

Just think about it, there are people out there that are paid to mathematically prove things and think of theories of numbers themselves.

Think about that next time you believe you've had an original thought.

Did you read the recent escapist headline where a 10-year old girl discovered a new molecule when she asked a question to her chemist teacher?

http://www.escapistmagazine.com/news/view/115697-10-Year-Old-Accidentally-Discovers-New-Explosive-Molecule

---

I think the worst thing to do is to think "people must have thought about this before" when you have an idea. Better to test it, experiment, think, share, talk about it than assume your own ignorance and defer to others mindlessly.

I believe this thread has been done before.
Next time, try to google your theory before posting it.

It would save you from half of this community being dicks towards you.

Zack1501:

gumba killer:
You can't divide by zero.

Why not?

Its Infinite how many times does any number go into zero? Infinity its called an Asymptote

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

anytime anyone ever thinks that they have "disproved math" they almost always have divided by zero somewhere along the way.

just saying, its one of the most overlooked mistakes it seems.

Kuroneko97:

Zack1501:

gumba killer:
You can't divide by zero.

Why not?

Oh God. If there was any doubts by anyone that you knew math, this just verified them.

This is a basic rule of math. Go back to Elementary school.

I figured this was going to be stupid the moment I read the title of this thread, and now I have been proven correct. Unlike your math.

Again, why not? I'm not saying its not true or that I don't know why, I want you to tell me WHY I can't.

Zack1501:

Kuroneko97:

Zack1501:

Why not?

Oh God. If there was any doubts by anyone that you knew math, this just verified them.

This is a basic rule of math. Go back to Elementary school.

I figured this was going to be stupid the moment I read the title of this thread, and now I have been proven correct. Unlike your math.

Again, why not? I'm not saying its not true or that I don't know why, I want you to tell me WHY I can't.

That's like demanding why I can't take the square root of the multiplication operator. It simply does not make sense with the terms involved. And why do you keep asking? There's a post right at the top of this page that says why in explicit detail.

x/0.5 = 2x
Which means that if I put all of my apples in half a pile I would get twice as many!

Just had to put that out there

Zack1501:

Vegosiux:

Zack1501:
So, I have an interesting math based question. If you don't like/hate math or don't understand basic algebra(I understand if you don't) just hit the big THE ESCAPIST logo in the corner and that will bring you home.

I wanted to know zero divided by zero equals. I tried to do at algebraically. This is what I did:

-The answer I was trying to get will be represented by x
0/0=x
-I times both sides by zero
0=0x
-This equals out to be 0=0 because anything times 0 is 0.
-This proves that x can be any number. for example if 5=x than 0=5*0 still is 0=0
-I rearrange 0=0x to be:
0/x=0
-Now since x can be any number now lets say x=0
-That makes this:
0/0=0
-And since x=0/0 (Right in the beginning^) and 0=0/0 also then x=0
-If you fallowed so far and remember that x can be any number then that means zero can also be any and every number. So 0 can now equal 5 or any other number.

I realize something is most likely wrong here.
So tell me escapist, Did i Disprove math?

Disproved math? No. Proved that you hardly know anything about math? Yes.

I bolded the part where you completely missed the point and made a conclusion that could only be characterized as and "ass pull", because 0/0 is an undefined expression.

So if 0/0=x and 0/0=0 then 0 does not equal x? I don't understand what you mean, please elaborate. I actuality want to understand why this is wrong past the usual argument of "Well you just cant divide by zero" That might be true but i have yet to find a person to tell me why I cant.

Dividing means putting something in a number of boxes (divide by 1, get one box of numbers; divide by two, number gets placed in 2 boxes;...). You can't put something in zero boxes. Some people claim you get infinity, but that's actually an approximation of the actual number that is used in slightly more complicated math with graphs and limits.

1. 0/0 looks like it should equal 0, but it does not. It is undefined, since you're dividing by zero. The rule is "if you divide by zero, it's undefined".

2. You say that "x can be any number". Well, yes, by definition it can be, that's why it's a variable.

3. You get to the point of "0/x = 0". This is not something where you need to bother with what x is or evaluating or plugging in for x--zero divided by anything is zero. But again, see point 1, since dividing by zero is always the exception.

4. You set up a specific equation and solved it for x. Even assuming that 0/0 = 0 and is not undefined, there is still absolutely no possible logical jump you can make to get from "x=0, so 0 can equal any number". It seems like you completely misunderstood the basic concept of a variable: a variableis something you use to stand in for a value or an expression. In this case, there is only value of x that satisfies your equation (again, ignoring the 0/0 problem), and you solved for it. Here, "x" can represent any number only in so far as it can represent any single number, which is already pre-determined by the equation. "x" does not mean "any number you like," it means "there is only one possible value for this, and I don't know what it is yet, so I'm just calling it 'x' until I figure it out." That value can be any value, yes, but "x" only represents that one individual value.

Zack1501:
So, I have an interesting math based question. If you don't like/hate math or don't understand basic algebra(I understand if you don't) just hit the big THE ESCAPIST logo in the corner and that will bring you home.

I wanted to know zero divided by zero equals. I tried to do at algebraically. This is what I did:

-The answer I was trying to get will be represented by x
0/0=x
-I Multiply both sides by zero
0=0x
-This equals out to be 0=0 because anything times 0 is 0.
-This proves that x can be any number. for example if 5=x than 0=5*0 still is 0=0
-I rearrange 0=0x to be:
0/x=0
-Now since x can be any number now lets say x=0
-That makes this:
0/0=0
-And since x=0/0 (Right in the beginning^) and 0=0/0 also then x=0
-If you fallowed so far and remember that x can be any number then that means zero can also be any and every number. So 0 can now equal 5 or any other number.

I realize something is most likely wrong here.
So tell me escapist, Did i Disprove math?
Edit: I see the error now. Its not that x equals 0 its that at one point x CAN = 0

You think that is interesting? Try this on for size.

infinity / 2 = 0.5 infinity = infinity
infinity + 0.5 infinity = 1.5 infinity = infinity
infinity / 0.5 infinity = 2 infinity = infinity
0.5 infinity = 1.5 infinity = 2 infinity = infinity

whole number (wn) infinity < real number (rn) infinity
yet wn infinity = rn infinity
because infinity = infinity

There are different sizes of infinity that are infinitely equal.
image

http://www.scientificamerican.com/article.cfm?id=strange-but-true-infinity-comes-in-different-sizes

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

Off topic- WTF?!?!?!?!?! How am I supposed to type Arabic?
image

Sorry double post.

And the virtual beatdown was immense. OP, keep your hopes up. The world is a nicer place than you might suspect by reading a gaming website thread. I was once thoroughly thoroughly convinced that my numerical method for deriving pi was correct. I actually said out loud, "Maybe pi is wrong." before I spotted my error an hour or so later. (This was from a college graduate with a 3.88GPa in mechanical engineering.)

I am glad that I did not have easy access to the internet back then to have made such a dopey statement in traceable written format. Don't give up on the idea that something can't be done just because nobody has done it. (Recent point in case: http://www.escapistmagazine.com/news/view/115697-10-Year-Old-Accidentally-Discovers-New-Explosive-Molecule )

[parting jab] 0/3 = 0/1 it follows that 1=3 [/parting jab]
Sorry. Sorry. I wanted to throw in some zero tolerance gibberish too.

FalloutJack:

Maze1125:

FalloutJack:
I believe it's fair that I started calling bullshit when we started on imaginary numbers, as though working with ones that actually exist wasn't good enough.

Imaginary numbers are just a name, they aren't actually any more imaginary than the real numbers.
Physicists use imaginary numbers to solve real problems every single day. Without imaginary numbers we wouldn't have the monitors you're using to read the posts people make on this site, they have very real and practical uses.

The same is true of a lot of maths. It may start as someone's "cool idea", but so many many advances in science have come from maths that someone just made up for the hell of it. If mathematicians waited until maths was useful before they came up with it, then our technology would be at least 50 years behind where it is today.

That part was actually a joke, the imaginery VS real bit. However, I'm going to need some citation on the part of you stating that imaginery numbers have an application beyond thought experiment. Since 'i' is literally representing a paradox, and that this is actually the tamest aspect of math acting less like science and more like philosophy, it smacks of carelessness. "We didn't feel like figuring out where this leftover piece of the puzzle actually comes from, so here, have a Lowercase-I." This is where math sort of falls short for me. I understand the logic you place behind it, pass the course, and move on...but it doesn't cry out as the pinnacle of precision anymore. And Discreet Mathimatics is very much this. It's the metaphysics of math that gives way to some interesting thoughts, but it's not logic and it's not science anymore. You follow my meaning, right?

The imaginary number 'i' (or 'j' in electrical engineering) is not a paradox. 'i' is a mathematical convention to represent the square root of negative one. The algebra and calculus involving complex numbers (all numbers with either real or imaginary parts) have been logically defined so that 'complex math' and 'real math' are logically compatible.

Using complex mathematics can be used to solve most of the integrals in the table in the back of your first year calculus book that you can't solve otherwise. Complex math is used in pretty much every type of science and here's the reason why it works: Any real quantity (mass, velocity, force, energy, etc) that one would want has to compute to a real answer, even if the math involves imaginary numbers.

Examples of where complex math is used for real world problems: Fourier Transforms (all science and engineering use to analyze the frequency dependency of data), expressing any cyclical or wave-like data as a complex exponential (electrical signals, light, springs) makes computation easier, and complex numbers is fundamental in quantum mechanics - which much of modern technology utilizes.

You need to go and study group theory and measure theory to a degree level and come back.

Arithmetic like that is not actually what maths is about.

Lord Beautiful:
Yes. You so totally disproved math. Because of this fantastic, unprecedented find, I think I shall sell my differential equations and quantum mechanics books to some poor sap who hasn't seen this brilliant proof. Lord knows I could use the extra cash.

Anybody else getting a troll vibe from this guy?

I'm getting more of a "13 Year Old that doesn't know what he's doing vibe".

If you have 0/0=X and multiply both sides by 0, then you have to multiply all numbers meaning that you'd still have 0/0=0x. So basically, you went around in a circle dude. Plus, greater geniuses have thought of this before and disproved it. Nice try though all the same.

Oops. Double post. Delete this.

You completely fail at math, because you can't divide by 0.

Now, time to blow minds.

.333... + .666... = .999...

(1/3)+(2/3) = (3/3)

3/3 = 1

.999... = 1

^ Actually true

The OP doesn't understand what zero is. It's the null set. You cannot divide by it for a very good reason--there is no content to the set to form a divisor (ergo a/0 literally has no meaning).

Long story short: OP, look up what zero means.

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