Division by zero is the operation of taking the quotient of any number x and 0, i.e., x/0. The uniqueness of division breaks down when dividing by zero, since the product 0·y = 0 is the same for any y, so y cannot be recovered by inverting the process of multiplication. 0 is the only number with this property and, as a result, division by zero is undefined for real numbers and can produce a fatal condition called a "division by zero error" in computer programs. To the persistent but misguided reader who insists on asking "What happens if I do divide by zero, " Derbyshire provides the slightly flippant but firm and concise response, "You can't. It is against the rules." Even in fields other than the real numbers, division by zero is never allowed.

complex infinity | complex number | C^* | division | extended complex plane | fallacy | field | limit | real number | reciprocal | ring | zero