LOCK I DUN LIKE ZERO

[ragnarok1945]

the rule is anything over the same number = 1, 0 is the only exception

[Guest]

yeah' date=' but if you say it's between 12 and 16 you're increasing the percentage of error because of the broader range.

[/quote']

 

The percent error of the final result is no greater than the percent error of the original uncertain value. 8/7 = 16/14, and 6/7 = 12/14; the ratios are the same.

 

If you do not have this much uncertainty in your calculation, then you already have more than one sig fig. The fact that you have no more than one sig fig ensures that you will have sufficient uncertainty to make the trailing digits meaningless.

 

This is how significant figures work; to say otherwise indicates the absence of a basic understanding of what a significant figure truly represents.

 

' pid='1444300' dateline='1228774137']

X/X = 1

 

X = 0

 

0/0 = 1

 

Explain to me why that does not work in this situation.

 

Look at it this way: the definition of division defines division as a binary function whose parameters are here called a and b. By the definition of division' date='

 

a/b = x <--> a = bx

 

And by a very basic theorem,

 

a = bx <--> a = b

 

Now, suppose b = 0. The equation "a = 0" is always true, regardless of x's value, if a = 0, and is always false, also regardless of x's value, if a =/= 0. Hence, division by zero always produces either no solution or infinite solutions. However, division is a binary function, and being a function it must always yield exactly one result, but when b = 0, the number of results is either zero or transfinite. Because of this, the cases where b = 0 are excluded from the domain of the function by definition.

 

This is why division by zero is always [i']literally[/i] undefined: the cases where the divisor is zero are prohibited in the very definition of division, since the failure to make this prohibition causes division to cease to be a function.

 

And, refuting your earlier "argument":

 

' pid='1441746' dateline='1228697972']

You have 0 pieces of cake' date=' and you have 0 people to give the cake to. Each person gets one piece of cake, since there are 0 of both factors.

[/quote']

 

Each person also gets 2 pieces of cake. While we're at it, each person gets negative twelve-and-a-half pieces of cake.

 

 

There are 0 people and 0 cakes. You cannot get 2 cakes, as there are only 0. Each person can get 1 peice of cake, since there are no people, and no cake to give. You cannot get a value of cake other than 1, because that value does not exsist.

 

What on earth is that supposed to mean? I have no people to give cake to, and since I have no people, I can give them each one piece, or five, or twenty, or negative seven, or no cake at all, or any other number that I feel like, and I will still be giving out exactly as much cake as I have available. There is nothing special about the number "1" that makes it and it alone work here.

 

' pid='1441746' dateline='1228697972']

Think of it this way' date=' you have 3 cakes and 0 people. Each person, there aren't any, get's infinite peices of cake. Each cake is distributed to 0 people.

[/quote']

 

Technically, this is undefined as well, but using limits and approaching zero from a positive amount of cake, it's fairly clear that the amount of cake given to each person is de facto infinite, and can be treated as such for practical applications.

 

' pid='1441746' dateline='1228697972']

But when it is 0 and 0' date=' each person must get 1, as nothing else applies to it.

[/quote']

 

What on earth are you blathering about now with this "nothing else applies to it" nonsense? 1 applies to it, 2 applies to it, and 27.269 applies to it as well, because zero times every last one of them is still zero, so every last one of them works.

[ragnarok1945]

actually it can be bigger. Say the final answer is 14.35 but the sig figs you can use is 1, so your answer is 10 (with 1 sig fig).

 

Now, if you use as many as you want (by using more than just the least amt of sig figs in the input numbers) and you get around 14, that's close to the actual answer

[Dark]

I still do not understand exactly what you mean by division by 0 creates none and infinte solutions, but when 0 is restrained to one solution, it is considered undefined. When b = 0, and it is a / b, sure, it is undefined. But when a = 0, it becomes, not the equation of...

 

X / 0 = Undefined

 

...but the equation of...

 

X / X = 1

[Guest]

' pid='1444423' dateline='1228775426']

I still do not understand exactly what you mean by division by 0 creates none and infinte solutions' date=' but when 0 is restrained to one solution, it is considered undefined. When b = 0, and it is a / b, sure, it is undefined. But when a = 0, it becomes, not the equation of...

 

X / 0 = Undefined

 

...but the equation of...

 

X / X = 1

[/quote']

In this case, the rule that anything divided by 0 is undefined overwrites (or creates an exception for) the rule that anything divided by itself = 1.

 

0/0 is an example of both X/X and X/0. As such, there are two possible answers, and the actual answer is the reconciliation of those 2 possible answers. X/X = 1 and X/0 = undefined. As such, there is no possible way to reconcile those two answers together, so the answer is undefined.

[ragnarok1945]

[Dark], it's not contradicting. When I say it's an exception, it means it does not follow the normal rules and therefore whatever normal outcome you're supposed to get, the exception can bypass this rule. That's why 0/0 =/= 1

[Dark]

' pid='1444423' dateline='1228775426']

I still do not understand exactly what you mean by division by 0 creates none and infinte solutions' date=' but when 0 is restrained to one solution, it is considered undefined. When b = 0, and it is a / b, sure, it is undefined. But when a = 0, it becomes, not the equation of...

 

X / 0 = Undefined

 

...but the equation of...

 

X / X = 1

[/quote']

In this case, the rule that anything divided by 0 is undefined overwrites (or creates an exception for) the rule that anything divided by itself = 1.

 

0/0 is an example of both X/X and X/0. As such, there are two possible answers, and the actual answer is the reconciliation of those 2 possible answers. X/X = 1 and X/0 = undefined. As such, there is no possible way to reconcile those two answers together, so the answer is undefined.

 

You said that neither of them are the answers, since there is one definitive answer. So how is undefined the answer, when that is the answer for X/0 = undefined? The answer would have to be based on opinion, which contradicts mathematics. Which means 0/0 equals NOTHING, not 1 nor undefined.

[Guest]

' pid='1444423' dateline='1228775426']

I still do not understand exactly what you mean by division by 0 creates none and infinte solutions' date='

[/quote']

 

0 * X = 1

 

0 * X = 0

 

The former is equivalent to dividing a nonzero number by zero, and has no solutions, since no value of X works. The latter is equivalent to dividing zero by zero, and has infinite solutions, since any value of X that you care to name works. Neither has exactly one solution.

 

' pid='1444423' dateline='1228775426']

but when 0 is restrained to one solution' date='

[/quote']

 

Division is a function, and functions by definition must yield exactly one solution for each input in the domain. Hence, division is constrained to exactly one solution at all times - the only way around this is to remove zero from the domain.

 

' pid='1444423' dateline='1228775426']

it is considered undefined. When b = 0' date=' and it is a / b, sure, it is undefined.

[/quote']

 

Good, at least you've managed to figure that much out.

 

' pid='1444423' dateline='1228775426']

But when a = 0' date=' it becomes, not the equation of...

 

X / 0 = Undefined

 

...but the equation of...

 

X / X = 1

[/quote']

 

"X / X = 1" only applies for nonzero X and has not (and can not, being false) be proven for X = 0. Your faulty reasoning derives from your inability to grasp that just because something works for positive and negative numbers, it does not necessarily work for 0, a number with the unique properties of an additive identity.

 

"X / X", where X = 0, equals whatever value of Y satisfies 0 * Y = 0; this is the definition of division. 1 certainly satisfies this. So does 2. So does 47. So does the square root of eleven. One value (zero) in the domain is producing multiple results in the range, defying the definition of a function; for this reason, you cannot divide zero by zero. I'm fairly sure that they teach elementary schoolers what a "function" is.

[ragnarok1945]

you can't have NOTHING as a solution, [Dark], nothing is technically still = 0, and 0/0 =/= 0, which means it has to remain undefined

[Dark]

Wait, wait, wait. Did you just say that...

 

X / X [X = 0] is the same as 0 * Y?

[ragnarok1945]

that's not the same thing. Multiplication with 0 is not an exception, as 0*Y=0, and vice versa, so 0*0=0

[Guest]

' pid='1444468' dateline='1228776240']

Wait' date=' wait, wait. Did you just say that...

 

X / X [X = 0'] is the same as 0 * Y?

 

Unlike multiplication and addition, division is not a fundamental operation inherent in the set of real numbers; instead, it is defined in terms of multiplication. Division, represented by the symbol A / B, is defined as a binary function which yields a unique result C such that BC = A.

 

In other words, the statement "A/B = C" is literally defined as meaning "A = BC", as long as C is unique (since it's a function, C has to be unique).

 

The problem is that, when A = 0 and B = 0, C is not unique; C could be anything satisfying 0 = 0C, and thus could be absolutely anything at all. This would stop division from being a function, which contradicts its definition. To prevent this, an additional clause in division's definition excludes the cases where B = 0 from the domain of the division function.

[Dark]

But 0/0 =/= 0*0. They are not the same equations.

[Guest]

' pid='1444485' dateline='1228776457']

But 0/0 =/= 0*0. They are not the same equations.

 

They are not equations at all; they are expressions.

 

Also, go read my last post.

[Dark]

So 0/0 equals infinite solutions, and that is considered undefined in the mathematical world? For example, if X equals all numbers greater than 1 [ X > 1], there is infinite solutions [just like in A/B, where A and B equal 0]. But X > 1 is not undefined, it is infinite solutions.

[ragnarok1945]

undefined does not mean infinite solutions, merely a solution we do not comprehend yet

[Guest]

' pid='1444504' dateline='1228776740']

So 0/0 equals infinite solutions' date=' and that is considered undefined in the mathematical world? For example, if X equals all numbers greater than 1 [ X > 1'], there is infinite solutions [just like in A/B, where A and B equal 0]. But X > 1 is not undefined, it is infinite solutions.

 

Division, by definition, is a function. Functions, by definition, cannot yield multiple solutions; there must be exactly one.

 

undefined does not mean infinite solutions' date=' merely a solution we do not comprehend yet

[/quote']

 

Stop. I am trying to help [Dark] here, and your insistence on posting false information is not helping at all.

[Guest]

' pid='1444504' dateline='1228776740']

So 0/0 equals infinite solutions' date=' and that is considered undefined in the mathematical world? For example, if X equals all numbers greater than 1 [ X > 1'], there is infinite solutions [just like in A/B, where A and B equal 0]. But X > 1 is not undefined, it is infinite solutions.

 

Division, by definition, is a function. Functions, by definition, cannot yield multiple solutions; there must be exactly one.

Also, X is not a function, so it doesn't follow the same definition.

 

Indeed; as defined here, X appears to be a set of real numbers.

[Guest]

' pid='1444504' dateline='1228776740']

So 0/0 equals infinite solutions' date=' and that is considered undefined in the mathematical world? For example, if X equals all numbers greater than 1 [ X > 1'], there is infinite solutions [just like in A/B, where A and B equal 0]. But X > 1 is not undefined, it is infinite solutions.

 

Division, by definition, is a function. Functions, by definition, cannot yield multiple solutions; there must be exactly one.

Also, X is not a function, so it doesn't follow the same definition.

 

Indeed; as defined here, X appears to be a set of real numbers.

Whoops, deleted my post on accident :P

 

Glad I got it right, though ;)

[Dark]

So there is only one answer to 0/0, since its function is of division, and since 1 is an inapropraite answer, and infinite solutions cannot apply to the function, the answer must be undefined. Tell me if I got that all right.

 

Now, undefined means that there is NO answer, or that there is no answer comprehendable to the human mind, so we have to make something up. Like imaginary numbers.

[Flinsbon]

OK here is a reason that 0/0 is undefined. Division is defined as the inverse of multiplication. For example...

 

12/3 = X. X = 4. We know this because the quotient times the denominator equals the numerator. 3x4 = 12.

 

Now, if 0/0 = X, we would get the answer by multiplying X times 0 to get zero. Now how do we know what to put in for X? Do we say X = 0? That works, but someone else can say X = 2. They are also right because 2x0 = 0.

 

Unfortunately, as a single variable, X can only hold one value, so we cannot define X. Therefore, 0/0 is undefined.

 

Now what if you put a different number in the numerator? Let's say 2. Now we have 2/0 = X. To find X, we would say 0X = 2. We would then say WTF? In this equation, we would never get a value for X.

 

This is why any number divided by zero is undefined. Any more questions?

[Guest]

' pid='1444540' dateline='1228777135']

So there is only one answer to 0/0' date=' since its function is of division, and since 1 is an inapropraite answer, and infinite solutions cannot apply to the function, the answer must be undefined. Tell me if I got that all right.

[/quote']

 

It's mostly right. Your one mistake is that you said that 1 is an inappropriate answer; on the contrary, 1 is a perfectly appropriate answer. The problem is that 2, 3, 4, 7, 18, and 570392 are also perfectly appropriate answers.

 

' pid='1444540' dateline='1228777135']

Now' date=' undefined means that there is NO answer,

[/quote']

 

Incorrect. It means that it is not defined - which, in practical terms, means that there is no unique answer. There are plenty of answers, but none is unique.

 

' pid='1444540' dateline='1228777135']

or that there is no answer comprehendable to the human mind' date='

[/quote']

 

That is utter nonsense produced by ragnarok, and should be ignored.

 

' pid='1444540' dateline='1228777135']

so we have to make something up. Like imaginary numbers.

 

No. Making things up here will not help at all. The first and most obvious problem is that we already have too many solutions, and nothing we invent can actually eliminate any of those solutions - we can merely add even more. It would be like trying to solve the problem of a sinking hot air balloon by placing an anvil in it.

 

I'll be offline for a while now; I'll respond to whatever you next say when I return. Take anything ragnarok says with a gallon of salt, since he's proven that he doesn't know what he's talking about here.

[ragnarok1945]

undefined and imaginary numbers are not the same thing here.

 

imaginary means non-existent number, whereas undefined is still a real number, just one we can't write out

[Guest]

undefined and imaginary numbers are not the same thing here.

 

imaginary means non-existent number' date=' whereas undefined is still a real number, just one we can't write out

[/quote']

 

See? This is an excellent example of ragnarok saying something that you should disregard.

[Dark]

Imaginary numbers are EXSISTANT.

 

The SQRT of -9, is 3i or -3i. It is a number and a variable, it just means nothing.

 

In this case, I don't understand what undefined means. There are infinite solutions, but the answer is restricted to ONE solution. Does that mean that the answer to 0/0 in itself is a contradiction, making it UNDEFINED?