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RSS FeedDivision by zero: Is it really impossible?
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| No | 46% | 566 votes | Total: 1219 votes | |
| Yes | 54% | 653 votes |
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Add to FavoritesIn the case of mathematics, a number cannot be divided by zero. If you divide by zero, then you are not dividing at all. The operation of division is struck null when dividing by zero because by its very nature, it has no value. For those naysayers, please note that the absolute value of zero is zero.
That being said, from the same point of view, you cannot really multiply a number by zero. It is a matter of perspective on the problem. A number multiplied zero times is not multiplied at all, in the real world. However, in the mathematical world we are taught a number multiplied by zero always equals zero, and a number cannot be divided by zero. In the mathematical world, this kind of makes sense, because you can rationalize that the division of zero cannot be computed and the multiplication of zero makes a number zero.
This is a case of mathematics deviating from practical application. How many times in life does one multiply or divide by zero? In the physical world, we can divide and multiply by zero. But, for the purposes of mathematics, especially for mathematics for programming, the multiplication of zero is entirely possible, and is used often for ease of reducing a number to zero for an array or other operations, even if this mathematics is flawed in real-world application.
So, we are left with how a number can be divided by zero. My sophomore year, I had a chemistry teacher who also taught physics and trigonometry. I had a conversation with him after a class and it somehow digressed and he spoke about the division of zero. He posed this hypothetical:
If you have a pumpkin pie, how man times can you lower a knife to cut the pie without cutting a new piece? The answer is that you could theoretically do it an infinite amount of times, by never cutting into the pie. So, in real-world application, division by zero is possible and can be performed. And what is the end result? One whole pie.
However, mathematics as it stands now says that multiplication by zero is possible and that division by zero is not. Are these mathematics flawed? Or is mathematics allowed to stray from the real world. Why is it that in the real world, you can divide by zero and the end result is equal to the initial number? By all logic, shouldn't any number divided zero times equal that number? In addition, shouldn't multiplication by zero also equal the same number as well, since if you multiply zero times, you aren't multiplying at all and thus not altering the original number?
Learn more about this author, Roy Malton.
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Yes
A question for all you math experts out there - is division by zero possible? On the face of it, the simple answer would seem to be no. Here's an example: "If you have three apples and no students, how many apples will each student get?" Well, the answer of course is none. Three apples divided by zero students yields zero; no one gets an apple because there's no one to get an apple.
This really doesn't answer the question of whether it is possible to divide by zero, a puzzle that has occupied mathematicians for many years. Using simple arithmetic or word problems doesn't seem to clear the matter up either. Nonetheless, let's give it a shot to see if we can come to some kind of conclusion.
Division, if you remember basic elementary school arithmetic, is a process of repeated subtraction until you have a number left that is smaller than your divisor. For example, 4 divided by 2. That looks something like this: 4-2=2-2=0. So, in two steps of subtraction you arrive at a number less than the divisor 2, the result is 4 divided by 2 equals 2. Division by zero, however, will never yield a result smaller than zero. It is a series of subtractions that never ends. For example, let's use the subtraction method to divide 4 by Zero and see what we get.
4 - 0 = 4 - 0 = 4 - 0 = 4, and so on to infinity ().
Let's look at it through an algebraic equation and see what it yields us:
Let a and b be equal to non-zero and a = b. a and b = 1, qed a = b = 1.
This is obviously an illogical answer, but let's take it one more step:
Let a and b = 1, a = b = 1
Then a2 = b, a2 - b2 = ab - b2
(a - b)(a + b) = b(a - b)
Then a + b = b, a = 0, and 1 = 0.
Again, an answer that fails the logic test as one cannot equal zero, and we're back where we began. The inescapable conclusion is that division by zero is a logical impossibility. Until a mathematical process is invented that can figure a way out of the endless loop that results from attempts to divide by zero, this is something that we have to accept.
Learn more about this author, Charles Ray.
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