TITLE: Will Division by Zero be Defined Eventually?
QUESTION [5 upvotes]: 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?

REPLY [6 votes]: 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:
$$a=b$$
$$a^2=ab$$
$$a^2-b^2=ab-b^2$$
$$(a+b)(a-b)=b(a-b)$$
$$a+b=b$$
$$2b=b$$
$$2=1$$