You mean that it's undefined? It actually makes perfect sense that it is left this way. Consider addition and subtraction as functions: f(x) = x + 42

You mean that it's undefined? It actually makes perfect sense that it is left this way. Consider addition and subtraction as functions: f(x) = x + 42 g(x) = x - 42 Now, realize that these functions are inverses of each other. Each one undoes the operation of the former: f(g(x)) = 42 + x - 42 = x g(f(x)) = x + 42 - 42 = x If you change 42 to any other real number, this relationship still holds. This is because f and g are functions that relate a number uniquely to another number. The inverse then, is just flipping that relationship (7 -> 49 has the inverse 49 -> 7). You can define similar functions for multiplication and division, and things will work out in the same fashion until you try to replace 42 with 0. What happens then is that the multiplication relationship is no longer unique. For f(x) = 0 * x f(x) is 0 for any choice of x! This is a problem when we try to flip the relationship as before to invert the operation. Since f(7) = 0 and f(49) = 0, should g(0) be 7 or 49? Moreover, the fact that the right and and left hand limit of 1/x as x -> infinity does not converge means that there's no obvious way to "plug the hole" so to speak and define 1/0 as some value.