Author Topic: Divide by zero  (Read 9689 times)

Offline Houshalter

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Divide by zero
« Reply #15 on: March 31, 2010, 03:17:00 PM »
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.

Offline Numsgil

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Divide by zero
« Reply #16 on: March 31, 2010, 04:19:43 PM »
Quote from: Houshalter
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.

Offline Houshalter

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Divide by zero
« Reply #17 on: March 31, 2010, 05:34:57 PM »
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.

Offline bacillus

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Divide by zero
« Reply #18 on: April 01, 2010, 03:40:23 AM »
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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Offline Numsgil

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Divide by zero
« Reply #19 on: April 01, 2010, 08:12:23 PM »
Quote from: Houshalter
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 or an 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.

Offline abyaly

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Divide by zero
« Reply #20 on: April 02, 2010, 07:22:31 AM »
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.
Lancre operated on the feudal system, which was to say, everyone feuded all
the time and handed on the fight to their descendants.
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Offline ashton15

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Divide by zero
« Reply #21 on: April 02, 2010, 02:11:40 PM »
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
« Last Edit: April 02, 2010, 02:12:22 PM by ashton15 »

Offline abyaly

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Divide by zero
« Reply #22 on: April 02, 2010, 05:05:54 PM »
Assigning meaning to a word is not the same thing as ascribing a property to an object.
Lancre operated on the feudal system, which was to say, everyone feuded all
the time and handed on the fight to their descendants.
        -- (Terry Pratchett, Carpe Jugulum)

Offline ashton15

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Divide by zero
« Reply #23 on: April 02, 2010, 05:17:37 PM »
Quote from: abyaly
Assigning meaning to a word is not the same thing as ascribing a property to an object.

What's the diffrence?

Offline bacillus

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Divide by zero
« Reply #24 on: April 02, 2010, 06:02:50 PM »
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.
"They laughed at Columbus, they laughed at Fulton, they laughed at the Wright brothers. But they also laughed at Bozo the Clown."
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Offline abyaly

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Divide by zero
« Reply #25 on: April 04, 2010, 02:31:58 AM »
Quote from: ashton15
Quote from: abyaly
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.

Quote from: bacillus
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.
Lancre operated on the feudal system, which was to say, everyone feuded all
the time and handed on the fight to their descendants.
        -- (Terry Pratchett, Carpe Jugulum)

Offline Houshalter

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Divide by zero
« Reply #26 on: April 04, 2010, 10:26:22 AM »
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.

Offline bacillus

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Divide by zero
« Reply #27 on: April 04, 2010, 03:47:35 PM »
Quote from: abyaly
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!
"They laughed at Columbus, they laughed at Fulton, they laughed at the Wright brothers. But they also laughed at Bozo the Clown."
- Carl Sagan