Whether division by zero is possible or not is a matter of metamathematics. Division is just a distribution of elements among a number of receivers. However, how many elements would you give to no receivers? The answer is simple. You wouldn't give any elements. This certainly makes sense. With this I can prove division of any number by zero equals to zero.
I would like to quote a famous statement: ex nihilo nihil fit (from nothing, nothing comes). This is yet another proof that x / 0 = 0, for any x, including infinite.
>>1
Your still wrong. Let's look at division intuitively another way. 6/2 = 3 means that we need to 3 groups of 2 elements to have 6 total elements. How many groups of 0 elements sums to 6 elements? There is no answer – no number of 0-element groups will ever equal up to anything (except 0, but that's where this intuitive illustration fails). Division by zero is not defined.
The limit from either direction (positive and negative) of c/x, where c is some constant, goes in different directions (one to negative infinity, the other to positive infinity). The limit does not exist, so c/0 is not defined. Stating that divising by zero produces zero is absurd, and the statement ex nihilo nihil fit in some sense supports the undefinability of division by zero as no matter how many zeros you took, you would never be able to add them up to the numerator, like the 4th reply stated.
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Anonymous2006-05-11 11:47
but a/0 = inf on the riemann sphere, because the riemann sphere only has one infinity.
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Anonymous2006-05-11 14:30
Let's see: if the limit from the right is +∞ and the limit from the left is -∞, then it makes sense to say the value of the division is 0, because it's the average of +∞ and -∞ , since average(+a, -a) = 0.
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Anonymous2006-05-11 19:35
the average is undefined.
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Anonymous2006-05-11 19:45
Why?
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Anonymous2006-05-11 21:18
(+∞+-∞)/2=0 -> ∞-∞=0
However, ∞+∞=∞. So, ∞-∞=∞+∞-∞=0?
You have to leave a lot of operations involving ∞ undefined to keep things consistent, so you might as well just leave division by 0 undefined and avoid the whole mess.
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Anonymous2006-05-12 1:16
It's average is irrelevant here, though impossible to compute since the arithmatic one would use on real numbers does not apply to infinities or undefined values.
You can't do arithmetic with infinity - so infinity + infinity does NOT equal 2*infinity, nor does it equal 3*infinity. None of those operations like multiplication or division have any meaning with infinity.
Infinity is defined as a quantity that is larger than all the real numbers -- arithmetic on it doesn't work.
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Anonymous2006-05-15 4:08
Thankyou >>20 :) I couldn't figure out the words to use to say that myself.
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Anonymous2006-05-15 8:34 (sage)
>>20,21
Bullshit. If multiplication doesn't have any meaning with infinity, then neither does addition.
It all depends on what you're working with. In the normal real line, there is no such thing as infinity. In the extended real line, ∞=∞+1=∞-1=∞+∞=3*∞=1.23*∞=∞/1.23, etc, etc.
Your failure at mathematics is a dirty scar on 4chan
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Anonymous2006-05-16 21:53 (sage)
Division by 0 = black hole. Everyone knows that.
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Anonymous2006-05-17 21:14
>>1
err.... which division are you talking about?... trying to pair mathematical concepts with real ones rarely works
ex: Division is not just a distribution of elements among a number of receivers, it is the inverse of an operation, which is just a function defined from RxR to R satisfying certain properties.
math is a game and it has it's own rules.. when you make out new rules, you start playing a different game.
going by your logic we can also define division as "how many times can i subtract the number a from the number b" (which is how it's usually explained to elementary schoolers) then, since i can subtract zero from any given number as many times as i wish, the division of any number by zero would be greater then any number i can give (not infinity mind you!). so, practically, it wouldn't be a number.