Even if there is an instance when there is division by number it should never return infinity. Lets say we examine the limit of 1/x as it approaches 0. As we approach 0 from the right we will get positive infinity but as we approach 0 from the left we get negative infinity. Thus, as we approach 0 we get two different sets of answers and we cannot return infinity. Furthermore, the solution set as we approach 0 contains numbers of ever increasing or decreasing values. So, returning Not a Number is not a valid return. Therefore, the only value that a 0 divisor should return is undefined.