Darwinbots Forum
General => Off Topic => Topic started by: triclops200 on March 30, 2010, 11:32:44 AM
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I did it, I divided by zero.... I built a set of non real numbers with a working correlation which allows one to divide by zero... I built a proof of this here... if you find a problem... let me know.
(http://images.yuku.com/image/x-png/d2e366804f6b9316d1d18ebff1c8addc7684e6c7.PNG)
Remember that 0n and 0n act like zero when working with real numbers but can have a correlation later if N0 appears, such as: 2*0*3 * 10 = 6
This should make it possible to solve 2x-6=0 in one step using the quadratic equation. (the normal way is easier... i know(2x=6::x=3), but still, this is just how it would work and possibly allow new math to occur)
*NOTE: I HAVE NOT FOUND WORKING PROOF FOR 0*A = 0A YET... I SPENT 7 HOURS TODAY WITH JUST THE NORMAL SETS AND 0A. WHEN I HAVE PROOF AND FOUND OUT COMPLETELY HOW TO WORK OUT ALL POSSIBLE PROBLEMS WITH IT I WILL LET YOU KNOW!
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Careful! You could destroy the universe!
Heres an interesting mathmatical thingy I found on youtube: Clikith here (http://www.youtube.com/watch?v=09vMTPFkcMI)
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I have proved 0A now as well.
KK New rule: 0A/0B = realnum A/B
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(http://images.yuku.com/image/x-png/1fb365d549f2917dd2298145ffb3ace58f23e252.PNG)
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Well... I worked for 9 hours today on how to divide by zero... well, the last 30 minutes have been depressing. I have proven that you cannot, unfortunatly, divide by zero... The one case Major equation I tried it on just happened to be the only one it worked with. I could try some more but I dought it will work, thanks to all of you who had the patience to read this post.
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Dividing by zero isn't new. Making up a new number that allows division by zero isn't an issue. If you look for them, I'm sure you can find plenty of number systems where you can "divide by zero". The problem is that we want the real numbers to be a field (http://en.wikipedia.org/wiki/Field_%28mathematics%29).
Like in every field, the additive identity (in this case 0), behaves in an unhappy way when we use it in multiplication. Namely, multiplying anything by zero just gives us zero again. So we can't undo multiplication by zero in a consistent way.
So the the real challenge for you isn't just to divide by zero. It's to divide by zero while still keeping your new number system similar enough to the usual one. But I still won't use it, since I think every single one of the field properties is more valuable than division by zero.
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That's what I was doing (I'm a clever 16 y/o )... It didn't work out, unfortunatly. I gave an example where it did, but that was just chance that out of all the equations that it could work, I hit it. I tried... I will probably try again tomarrow, this time from a different angle, but I have serious doughts that it can be done. Though getting one example is a positive step in that direction. But the problem is: The new set of imaginary numbers will have to contain rules that either conflict with real number 0 rules or make an endless set of imaginary 0 rules.
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Okay, so you're saying dividing by zero results in the entire real number set?
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No, it equals an undefined imaginary number which has some similarities to the real number set and follows alot of correlations, but is undefinable and utterly hard to work out...
1/0 = 10
2/0 = 20
0/2 = 0 right? well it also equals, in my rules, (which were incorrect, but it was still a beautiful system untill I figured that out) 02
0/3= 0 and = 03
0*2 = 0 and 02
0*3 = 0 and 03
I actually got a correct answer from it once, using 0 as a value, but I tried 4 more similar equations and none of them were correct. I am going to start again tommarrow, but I am making no promises on weather it can be done.
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I am almost through with algebra 2 at my school and I still can't figure out what your talking about. But this does give me an idea. Ever hear of AM (http://en.wikipedia.org/wiki/Automated_Mathematician)? Its an old artificial intellegence program that did math. Theres also automated theorem proving (http://en.wikipedia.org/wiki/Automated_theorem_proving), which I guess is similiar. My idea is to use a program like that and set it loose on trying to come up with useful concepts and properties related to division by zero. Or you can always do what you did and waste 9 hours of your life.
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For the record, the forum should support latex. So you don't need to embed images (I'm assuming you're using latex to generate them, or can get latex out?).
eg:
[img class=\"tex\" src=\"http://www.forkosh.dreamhost.com/mathtex.cgi?2/0 = 2_0\" alt=\"LaTeX: 2/0 = 2_0\" /]
The magic is using the tex tags
This is what the field of Abstract Algebra deals with. Abyaly linked to one important concept called a "field". I'd recommend that you try doing a bit of research about fields and the like before you delve too deeply into this. It'll help you formalize your concepts. Don't do it through wikipedia, though. The math articles are always only useful if you already know what they're talking about. They are a pretty bad introduction to the concepts. Instead of starting with fields, start with groups. They're about the most basic building block in abstract algebra.
If you don't do that AA research, you're just spinning your wheels. Like someone trying to harness the power of lightning without studying electromagnetism in a physics text book.
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Careful! You could destroy the universe!
Heres an interesting mathmatical thingy I found on youtube: Clikith here
You can't cancel out the terms in the last step. Even though they look equal, x and y might be 0 and then you'd end up dividing by a zero.
Not sure if you knew that was the mistake already, but wanted to point that out.
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That's right - the biggest trap in these proofs is often that people assume that (x^2)/x = x.
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When is x^2/x not equal to x? Even if x is zero then its still zero.
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If it's zero... it's undefined... that's what I wasted 9 hours finding out the hard way, but I'm still working on it, lol. Even 0/0 still equals undefined... for now.
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No, 0/0 can't be undefined. I think it could have multiple answers, but it can be zero for example. See, if you take 0 and multiply it zero times you get zero. So in reverse you get the same thing. Heres the real problem: x/0=y. If you use traditional math on it, you get x=0. But what if x isn't equal to zero? Its because 0(anything) is always equal to zero, even if its x/0. But then that means that the rule where you multiply both sides by the same thing is invalid. Now where back to where we started. Its a circular problem that depends on its self for an answer. Good luck though.
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No, 0/0 can't be undefined. I think it could have multiple answers, but it can be zero for example. See, if you take 0 and multiply it zero times you get zero. So in reverse you get the same thing.
If you do x/x, it's 1 for all real numbers except for 0. So another way to look at it is to take the limit and then 0/0 becomes 1. Point is there are lots of different rationalizations you can use to define 0/0, but they don't all agree with each other. That's what it means to be "undefined". Or rather, undefinable. There are multiple competing and contradictory definitions.
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Huh. You made me think .
I had an idea today while thinking about this problem. Its simple: Zero isn't a number. Its a symbol, a visual aid to represent a concept. Its not an actual number. We invented it as a useful place holder so that we didn't have to invent a new symbol for 10, 50, 100, etc, like most ancient people did. Think about it, it litteraly represents the lack of a number, not a number itself. Its own properties conflict with the properties numbers have. Take any number and add zero, it doesn't change because zero isn't a number. Its like not adding in the first place. Take an number and multiply it by zero, you get nothing because you litteraly take that number zero times, like not taking it at all. You can't have zero of something, because if you did its the same as not having it at all anyways. Its because zero is a symbol, not a number, it gets confusing when you treat it like one. Its like trying to dividing 1,000 by the at (@) symbol. It just doesn't make sense. So its no wonder what happens when you try to find out how many times nothing fits into something, even if that something is nothing in the first place. It can't be done.
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If it helps, take the opposite as an example - when you solve a polynomial, for example x(x-2)(x+5)=0 , then it would be arithmetically correct to divide by any of the factors eg. 0 = x(x-2) could be considered equivalent and logical after dividing through by (x+5). But you'll have gotten rid of a solution, and thus altered the formula, and by carrying on further, you'll eventually end up with 1=0. The point is that wierd things happen at zero, even though they seem to make sense-you're essentially modifying the equation in a geometric sense, and if zero is the 'pivot', it's difficult to realize when the result becomes illogical.
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Huh. You made me think .
I had an idea today while thinking about this problem. Its simple: Zero isn't a number. Its a symbol, a visual aid to represent a concept. Its not an actual number. We invented it as a useful place holder so that we didn't have to invent a new symbol for 10, 50, 100, etc, like most ancient people did. Think about it, it litteraly represents the lack of a number, not a number itself. Its own properties conflict with the properties numbers have. Take any number and add zero, it doesn't change because zero isn't a number. Its like not adding in the first place. Take an number and multiply it by zero, you get nothing because you litteraly take that number zero times, like not taking it at all. You can't have zero of something, because if you did its the same as not having it at all anyways. Its because zero is a symbol, not a number, it gets confusing when you treat it like one. Its like trying to dividing 1,000 by the at (@) symbol. It just doesn't make sense. So its no wonder what happens when you try to find out how many times nothing fits into something, even if that something is nothing in the first place. It can't be done.
You can, by definition, remove 0 from the real numbers. But then you have an unfortunate problem with addition, since there wouldn't be an additive identity.
Which means real numbers under addition wouldn't be a "group", because it wouldn't have closure (http://en.wikipedia.org/wiki/Closure_(mathematics)) or an identity element (http://en.wikipedia.org/wiki/Identity_element). Without group status it loses a lot of the nice properties we need and expect in algebra, so it suddenly becomes much less useful.
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Houshalter, all of the numbers are made up. Zero is just as much of a number as any of the others.
Also, you are philosophizing over the "correct" meaning of the word "number". There is no such thing as a "correct" meaning to a word. As with any word, its meaning comes from the intent of the people using it in conversation. For two people to have a meaningful conversation about X, they first agree on what they both want X to mean, and then they say things about it. If this isn't done, you end up in a situation where person A is attempting to say one thing and person B is interpreting it as something else.
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But surely it doesn't matter wether I intrpret that the Earth is really an orange as to wether that fact is true or false and likewise if the interpretaions of imaginary numbers has been defined the way they are you can't just understand them to be something which is ilogical and expect it to be true whilst fitting in with the original interpretation. Thus if I create the intrepretation is a purple gurble then the intrepretaion of a gurble bieng orange would not fit the current intrepetation and would therefore be false, though if one said the gurble had tremendously big eyes in conjuction with a fondness of striped ties then they could be true or flase depending on there proof and then again it may be possible for the gurble to be orange if one were to weave through the intrepetaion and justify that the gurble was not purple so he may be another colour or striped purple and orange but wouldn't it be a shame if our gurble was not purple? Woot! Crappy rhyming and some nonsense philosphy at the same time
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Assigning meaning to a word is not the same thing as ascribing a property to an object.
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Assigning meaning to a word is not the same thing as ascribing a property to an object.
What's the diffrence?
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There's a proof by somebody whose name eludes me at this moment that states that if mathematics is without contradictions, then it is contradictory itself. Don't ask me how it works, but I thought this would be the best time to bring it up.
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Assigning meaning to a word is not the same thing as ascribing a property to an object.
What's the diffrence?
The first is saying something about a word. Specifying what object or concept you're going to use that word to refer to.
Eg: "The word gold refers to the element with atomic number 79"
The second is saying something about the object or concept the word is referring to.
Eg: "Gold is yellow"
The reason you can define a word to be whatever you want is that a definition says -nothing- about the object the word is referring to. It doesn't even guarantee such a thing exists. A definition is a statement about the person who is making it. If I define the word "splaz" to mean "gold", this doesn't say anything about gold. All it means is when I say the word "splaz", I'm talking about gold.
So if you define the word "Earth" to mean the same thing as the word "orange", this doesn't mean that the thing I think of as the Earth is the same thing as an orange. It means that when I see you use the word "Earth", I should think of it as if you had said the word "orange" instead.
There's a proof by somebody whose name eludes me at this moment that states that if mathematics is without contradictions, then it is contradictory itself. Don't ask me how it works, but I thought this would be the best time to bring it up.
You are probably thinking of Gödel's incompleteness theorem, which says no consistent set of axioms can prove its own consistency.
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I was trying to think of a way to define number in strict logical terms that could be used by a computer. Its not as easy as it sounds. You might say that a number is or represents a single value, but how do you define a value? Maybe you can take a short cut and define a number as a set of binary digits, but thats not an actual number. It just represents a number, and were back to the same problem.
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You are probably thinking of Gödel's incompleteness theorem, which says no consistent set of axioms can prove its own consistency.
That's the one!