This is something I have thought quite a lot about. There are many opinions on the subject. I think most mathematicians would agree that it is impossible or at least senseless to divide anything by zero. For if you divide ten cookies evenly among two people, each will get five; but how in the world are you going to divide them evenly among zero people?
Then there is the logical idea (which I invented for myself) that any number divided by itself makes 1. So 0/0 = 1, for zero goes exactly once into zero - or does it? One could also say it goes into zero an infinite number of times. This would go for any number divided by zero, if it weren't for the fact that you will never arrive at, say, one, no matter how often you multiply an infinite number by zero, as anything multiplied by zero equals zero. You only need to multiply zero by zero, however, to arrive at zero. So 0/0 equals anything from an infinite negative number to an infinite positive number.
But here I make the mistake of considering infinity a number. It is not. In fact, I believe there is no such thing as infinity. "An infinite number" is a contradictio in adjecto because a "number" is by definition a definite number. Indeed, I believe that infinity *equals* zero! For there is no such thing as infinity, and there's no such thing as zero... Even more unsettling may be that I think there is no such thing as "one", or "two", or rather, they are merely abstract concepts. For as soon as we make them concrete - for instance, by saying "one apple plus one apple equals two apples" -, we have supposed that these two apples are equal - that there can be "equal things". Each apple is unique, so it's a case not of a + a but of a + b. And whereas a + a is, as you know, = 2a, a + b is simply = a + b; no simplification is possible. Mathematics is a simplification: it supposes similar things to be "the same". But there's no such thing as sameness. Indeed, there is no such thing as a "thing"; there is only relative duration, relative unity within the flux.
2006-06-27 00:06:26
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answer #1
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answered by sauwelios@yahoo.com 6
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If you had asked in the mathematics section, you may have received more enlightening answers. The simple answer is that 0/0 is undefined. Although infinity is also "undefined", that does not necessarily mean that 0/0 is infinite. It may be, or it may not be. This type of equation is known as "indeterminate" (as is infinity/infinity).
People have been pondering this for quite a while, and limits help provide the answer. Consider the following equation at x=0, which evaluates to the indeterminate form "0/0":
(3x)/x
Because x/x = 1, this can simplify to 3. So, it may be tempting to say that (3x)/x = 3, but this is NOT true at x=0 because 0/0 is undefined. However, we CAN say that "the limit of (3x)/x as x approaches 0 is 0". This is basically saying that if (3x)/x DID exist at x=0, it would be 3. This concept is explored in first-semester calculus courses.
Here is another example:
(3x^2)/(5x) at x=0
We can divide out an x and convert this expression to "(3/5)x", which, at x=0, is 0. So in this case, 0/0 would be 0 if it existed.
One more:
(2x)/(x^2) at x=0
We can divide out an x from top and bottom, resulting in the expression "2/x", which is infinite at x=0. So, in this case, 0/0 would be infinite if it existed.
These equations were all simple examples. More complicated examples can also be evaluated using l'Hospital's rule (see sources below).
2006-06-27 10:12:56
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answer #2
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answered by HCP 2
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Let's say 0/0 is some number n. Multiplying both sides of the equation by zero...
0/0 = n
0 = n x 0.
This presents a problem, because n could be any number. So 0/0 has no unique value. The only conclusion that we can draw is that division by zero is "undefined", or meaningless.
2006-06-27 16:38:54
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answer #3
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answered by Polymath 5
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Actually mathematically you cannot divide by zero,
so the expression 0 / 0 has no meaning.
The answer 0 is kind of right (but still wrong) because:
for the funtion 0 / x
as x approaches 0, 0 / x approaches 0
or in calculus terms, the limit of the funtion 0/x as x approaches 0 is 0.
2006-06-27 06:32:44
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answer #4
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answered by Matthew D 2
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0/0 is divided to zero because your product is the same as your beginning numbers which are 0/0
2006-06-27 06:02:47
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answer #5
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answered by animewarlord5000 2
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Well, every scientist declares that the operation "0/0" doesn't lead to any result: indeterminated. "Nothing can be divided by zero".
You can only get something like "O/x", with x coming closer and closer to zero.
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Anyway... Factorial(zero) = 0! = 1.
So, you can declare without any doubt that: "0/0! = 0", but you cannot say that: "0/0! = 0!"...
2006-06-27 08:04:58
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answer #6
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answered by Axel ∇ 5
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are you asking "prove the quotient of 0/0" or saying "0/0= x"? Whichever: zero divided by anything is exactly 0.00, even if the dividend is zero. In this case though it is -5: you spent 5 points on that one. the THEORUM however in every other case is; in dividing any real number,not zero, as the divisor aproaches zero, the qoutient aproaches infinity. OR; 0/0 = 1 WHOLE NOTHING, AND ANY NUMBER OF NOTHING IS STILL NOTHING, EVEN AN INFINITE AMOUNT OF NOTHING IS NOTHING..
2006-06-27 07:05:55
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answer #7
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answered by mr.phattphatt 5
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0/0 =0
2006-06-27 06:04:29
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answer #8
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answered by R S 4
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This ---> ( / ) is a sign meaning division or divided by in computer speak, just as ( * ) means multiplication. Therefore, 0/0 would mean zero is divided by zero which leaves nothing, as nothing divided by nothing would give you nothing. Here, zero being of no value.
2006-06-27 06:02:11
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answer #9
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answered by Natalie 3
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It has to b ummm...... 1 coz, 0 multiplied by 1 gives 0.so if u divide 0 by 0 d answer will b 1.
2006-06-27 06:02:28
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answer #10
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answered by Anonymous
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