>Note: you are not allowed to divide by zero. The result would be meaningless if you could. And 'NaN' is only something the computer spits out when it encoun

>Note: you are not allowed to divide by zero. The result would be meaningless if you could. And 'NaN' is only something the computer spits out when it encounters an operation that doesn't return a number. Usually, a computer will give you 'Inf' when you try to divide by zero numerically. Mathematically, you cannot do it. So don't try. That is not true. You can mathematically divide by zero, just not over the Reals (or any other nonzero commutative ring). There is no reason that you cannot define a number system where division by zero is allowed, however in doing so you loose some nice properties that we enjoy about the Real numbers. A common example from math is the real projective line (which adds a point at infinity, and defines that a/0=infinity when a=/=0). Another commonly used number system that defines division by zero is the IEEE floating-point standard. In fact, IEEE defines division for all values of 0 (it has a positive and a negative 0). Specifically: a/+0=+infinity | a>0 a/+0=-infinity | a<0 a/-0 =-infinity | a>0 a/-0 = +infinity | a<0 0/0 = NaN | for any combination of 0 values These definitions would cause floating point arithmetic to loose some nice properties of the Reals, however it provides the property of division being defined everywhere, and other decisions made already caused floating point arithmetic to not have the properties.