Will Division by Zero be Defined Eventually? [duplicate]

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?

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:

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

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 :)