This is for the *genuises*. when posed with the problem, "what is the answer to 0/0?" i have come across three different solutions and im not sure which is correct:
1. since any fraction with 0 as the denominator cannot be solved, then the answer is "undefined"
2. since any fraction with 0 as the numerator is zero, then the answer is "zero"
3. finally, since any fraction in which the denominator and the numerator have the same numerical value is equal to one, the answer must be "one"
so which one is correct?
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Anonymous2007-07-01 15:09 ID:xugRnLct
Answer is DNE, now GTFO
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Anonymous2007-07-01 15:13 ID:fxhdLsot
>>1
Depends on the context. The answer can be 9000 if I want it to. L'Hopital's innit.
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Anonymous2007-07-01 15:45 ID:5BWgas6f
>>2
So, if I have an equation that can be simplified to:
Like 9 said, but slightly differently:
DNE is shorthand for a logical statement, "the set of solutions is empty", or "the solution does not exist".
NaN and +-INF are machine specifications for values that fall outside the range of finite machine numbers. They are placeholders used so that the variable containing the solution to an equation can be specified to exist, without actually having a (finite) numerical value.
Limits where both numerator and denominator approach zero _can_ have any complex value (depending on the limit) or be undefined, but the "fraction" 0/0 just doesn't make any sense because zero doesn't have a multiplicative inverse (you might as well ask "What's the numerical value of zero divided by true love?").
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Anonymous2007-07-02 14:21 ID:Gv6LkwUy
>>13
So DNE is pretty much like Ø, and it can be said that 0/0 = Ø?
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Anonymous2007-07-02 17:27 ID:p+paQ/iJ
the answer is undefined, or DNE, division by 0 supercedes a numeratot of 0.
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Anonymous2007-07-02 17:29 ID:KCoqNVgZ
if x/0 = inf than inf * 0 = x ? This means inf * 0 = all posotive rela numbers? Wrong. It is not an inequality and remainds undefined
Niggers, that is for when you are taking a limit and the limit becomes 0/0 (same with l'hopital's rule). As for the expression 0/0 or inf/inf, it simply does not exist. Now go kill yourselves.
>>16
No, they're... They're doing it wrong.
0/0 is undefined, and is part of a group of indeterminate forms (such as 0^0, inf/inf, etc.). 0/0 does not equal DNE. DNE is what you get as the result of taking a limit that doesn't actually exist.
Example:
The limit of 1/x as x approaches 0. Looking at the graph of 1/x, you can see that coming from the left, 1/x approaches -inf. Coming from the right, it approaches inf. Because there is a disparity where the two meet (i.e. it is both infinity and negative infinity), the limit is said not to exist.
You can't use NaN or DNE in any sort of equation; they're just what you get when you've screwed up somewhere.
no the number 0/0 is not a real number. Let's go back to basic math.
Numerator: How much out of a piece of something or part there is.
Denominator: How many parts of a peice of something there are.
Now using those definitions for the fraction 0/0, lets define the fraction. The denominator is 0. That means there is 0 parts to nothing. It isn't going on for infinite, there are no parts to it for it to go on for infinite. Now for the numerator, the numerator divides out of the denominator as we all know from the definitions (remember, it is how many parts out of the whole, and the denominator is how many parts there are). So, if there aren't any parts, then there is no numerator. So this fraction is non-existant. That is why this is not a real number.
Now you are going to ask, what does it equal? Well, if it's not a real number, nothing! hahaha, non-real numbers don't equal anything because they are either errors in equations or things like infinite or etc. So, I hope this ends this <_<
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Anonymous2007-07-03 15:26 ID:5l7f+9pj
has anyone ever heard of the box analogy to describe divide by zero operations? i think its very good way to 'visualize' why you can't divide by zero.
>>24
I have difficulty understanding your reasoning. In any case, it is not true that "non real numbers don't equal anything". i is not real, and is very well defined. 0/0 is not well defined.
"0/0 is undefined, and is part of a group of indeterminate forms (such as 0^0, inf/inf, etc.)"
Congratulations. There are 27 posts on this thread, and you're all fucking morons.
x/0 for x != 0, is undefined.
0/0 is indeterminate, NOT undefined.
indeterminate != undefined.
l2/math/ before you fucking post shit to do with it.
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Anonymous2007-07-07 19:37 ID:8gmw+U/F
It is indeterminant.
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Anonymous2009-03-18 3:12
I feel the need, the need for weed!
Marijuana MUST be legalized.
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Anonymous2010-10-07 10:35
According to Euler: 1/0 may be undefined but 2/0 is twice that number. But he was a little crazy.
According to Hardy: any number divided by 0 is meaningless.
But really, we all know that the expression 1/0 is really meaningless, but the right hand limit of 1/x as x -> 0 = infinity. There is no argument here (I hope). Can we now agree that 0/0 is the same as 0 * (1/0) which is meaningless? Or can we write 0/0 in a way which is meaningful, or can we write it in a different way which allows us to make some sort of conclusion about what it's meaning is?
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Anonymous2010-10-07 10:38
Or one can just point out the fact that division by zero is not allowed in the field of real numbers, and we can just leave it as that. So (any real / 0) is undefined in the field of real numbers.
Your 3rd assertion is incorrect -- it must exclude fractions whose denominator is zero, i.e., 0/0. This is because of your 1st statement: Division by zero (including a fraction whose denominator equals zero) is undefined for real numbers and most other number domains.
The "fraction" 0/0 is therefore undefined and as such has no value. However there exist limits of the form x/x where x approaches zero. The form is said to be indeterminate and it's corresponding limit may exist and have any of various values, depending on the original expression.