Why is Division by Zero Not Possible?

[Giulio B.]

i'm a hight school student and this is a stupid question:

why "3 x 0 = 0" and "3/0 = nothing"? should make 0 too.

it bothers me from years

 

[TD]

"3/0" is not 'nothing', it is left 'undefined'. Why should it be zero?

 

[tmc]

division by zero is undefined.

Division is defined as multiplying by the inverse. Say you write a/b = x, you actually mean a * b^(-1) = x, where b^(-1) is defined the be the unique number such that b * b^(-1) = 1 = b^(-1) * b.

However, 0^(-1) does not exist: suppose it did. Then, 0 * 0^(-1) = 1. But for any a, 0 * a = 0. Hence, we have an obvious contradiction.

Thus, saying a/0 = a * 0^(-1) = x is completely meaningless, since 0^(-1) does not exist.

 

[Crusty]

you can't divide 3 staws into zero groups.
You could divide them into 1 group of 3, or 3 groups of 1, or others if you cut the straws into smaller pieces. No mater how small the pieces there will just be more and more groups.