I was quite disappointed to read a BBC news story about the a new “theory” that supposedly solves the difficulty of dividing zero by zero (thanks to the blog “Web Pruned by Dawdling Monkeys” for pointing it out). The article discusses a Dr. James Anderson from the United Kingdom who has declared that this value should be called “nullity” and that with this definition, he has solved a “1,200-year-old problem.” While I was annoyed enough to write about it myself, I would actually recommend you read more about this incident at “Good Math, Bad Math,” which is much better written than what I could do.
First, some background. In mathematics zero divided by zero is considered indeterminate (and is undefined, as well). In approximate lay terms, this is because if we try to evaluate it in different ways, we get different results. In general, division by zero is not defined in mathematics. One way to look at this is to think of division as the inverse of multiplication. When we ask what twelve divided by three is, another way to word it would be to ask what number, when multiplied by three, gives twelve.