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Possible Duplicate:
Division by $0$

I've always been inclined to believe that x/0 = NaN is a placeholder for a character or constant that no one has created yet.

I know assume that none of you can tell the future, but is there an expectation that someone will eventually (successfully) define division by zero?

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    This "Weel-theory" does not convince me!2018-08-02

2 Answers 2

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Division by zero can be defined. It is called Wheel Theory. It's not a very popular set of mathematics and the paper that it originates from is a little difficult to find. Division by zero is left undefined in modern mathematics because it causes a loss of many useful statements. For example, $\frac{a}{b}=c \Rightarrow cb=a$. This is not true when $b=0$ and $a$ is nonzero. ($cb=0\neq a$) So, we lose generality by allowing division by zero to be defined.

Allowing division by zero also leads to proofs such as this which are valid:

$a=b$ $a^2=ab$ $a^2-b^2=ab-b^2$ $(a+b)(a-b)=b(a-b)$ $a+b=b$ $2b=b$ $2=1$

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    Is this "Weel theory" widely accepted at all ?2018-08-02
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My understand of arithmetic division over R is this: a/b = {x in R| b*x = a}. In case of division by 0, the answer would be none unless a = 0.

By studying the limits of the function 1/x we can tell that 1/0 is the biggest number ever(which is known to not exists :))

What I wanna say, is that 1/0 doesn't exists and thus cannot be defined. Unless..who knows :)