This is possibly the most commonly asked question by students to teachers in a mathematics lesson. It is a question that enables the minds of millions of students everyday. Following just basic laws and rules of mathematics, that any number divided by itself is one, zero divided by zero should be by all means equal to one. However there are exceptions to every rule.

We take any integer other than 0 and we divide that by itself and you get the answer of one. Why is that so? It is because there is something that exists shared amongst an equal number of something that exists. If you take any integer other than zero and divide that by any other integer other than zero and you will get an answer, rational or irrational. That is because there is an existence of a particular thing. If you take zero however, zero does not exist. There is NOTHING to begin with so you have nothing to share. You can share this nothingness with as many people as you want, and they will all be receiving absolutely nothing. So this can be done an infinite number of times and we call this infinity. So you can't divide zero as there is nothing for you to divide, thus making it impossible to do so.

If we take the case of dividing zero by itself, well following the concept, since there is nothing for you to divide in the first place, there is also nothing there for you to divide it to. So you end up with this semi-paradoxical situation where you have nothing and can give to nothing. So this is more or less than given the term undefined. There is no reasoning or logical explanation behind this concept as it cannot be explained as it will not make sense or follow on. So dividing zero by itself will not give you one but only a term of undefined as where as dividing anything else by zero gives you infinity.

Dividing by zero is not possible as it will not give you an answer thats workable with. No matter how hard you try, it does not allow you do such a calculation. Zero in the denominator or the divisor can be called the asymptote. It is a limit of infinity. You can divide zero by the number as much as you want and you will never ever get an answer and you will never ever get anywhere close to an answer. You will get nowhere. It just can't be done. Well you can argue that its a number but it is a special number. Same with infinity. There is no definite meaning. So zero is physically impossible to divide and expect anything other than infinity or undefined. Those are the only two possible answers one may get or expect when dividing by zero.

But all of that is by defining physical division of zero. It is not all that impossible. It still can be done and you can end up with numbers which are imaginary. It just makes working with harder. Defining impossible is having no particular method at all that can arrive at an answer. Well since you have a special answer of imaginary then its one step towards finding an answer which involved dividing something by zero. That something which you can use to divide by is perhaps another infinity or another imaginary number. That is what can make it possible due to the fact that your working with numbers that physically don't exist but in theory it does. As long as you can do it by theory by introducing all sorts of imaginary numbers of i or perhaps even placing root signs around it, modifying it as you went, gold will eventually strike. Since not ALL methods have been tested yet, we cannot say it is impossible.