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Unread 09-08-2005, 12:38
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Re: impossible statements

Here's my argument:

If we go back to the elementary school definition of division, we can say that in division, the answer is equal to the size of each part when something is divided into a certain number of parts. In other words, if we have the expressions 12/3 = x, x is 4 because when 12 is divided into 3 parts, there is four in each part. Also, x is the number of times that 3 goes into four.

In another definition, when we have the equations x/y = z, then z is the number that you can multipy by y to get x. In other words, if 12/3 = z, then z = 4 because 4 is the number you can multiply 3 by to get 12.

Having those two definitions to use, we can look at the problem of dividing by zero. When we ask, "What is 5/0?" we do not come up with an answer because there is no number that you can mulitiply by 0 to get 5. This is the main reason why the rules of algebra do not allow you to divide by zero.

In the 1 = 2 proof above, it is true that one step divides by zero. However, in that step, the numerator is also zero. Let's look at that situation:
0/0 = ?
What number can we multiply by zero to get zero? Any number!
And this is why I say that 0/0 = 0/0 can give you 1 = 2.

Even though this proof is logically valid, the idea that 0/0 is not practical in Algebra. This is why the rules of Algebra say that you cannot divide by zero, even when the numerator is zero.The fact alone that 1 does not equal 2 is enough reason that it will ultimately be said that this proof (and others like it) are useless.

I still think it's a fun idea to play with.

Now, what about the second proof?
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