(Disclaimer: This post is merely trying to describe why result of division by zero sometimes written or assumed as infinity. It does not describe detail mathematical aspect of zero division. )
We usually say it is not possible to determine the result of zero division. Sometimes we write the result as an infinite number. In my early days of math education I always wondered why we say it undefined and write as infinity in mathematical expressions. One possible reason is to assume infinity itself as an undefined number or entity. But there was another explanation.
To understand what happens when something is divided by zero, lets make some divisions. Suppose we will divide two by some numbers. If 2 is divided by 1, the result is 1. If 2 is divided by 0.5, result is 4. If 2 is divided by 1/3, a smaller number than 0.5, result is 6. This is a bigger number than 4. In this way if you continue to divide by smaller numbers, result will continue to grow as well. Therefore we can conclude that division by a number close to the smallest positive number, which is zero, will produce a result close to the biggest positive number, which is infinity in this case. We do not need to know the actual value of infinity in this case for any reason.
It is important to note when result if division is written or assumed as infinite number, total calculation becomes an approximation and better be dealt using limiting expressions of calculus.
I hope my explanation was easy to understand. I am not claiming it as flawless, though I think it is not a wrong explanation in any way. If you have anything to ask about this explanation, feel free to use the comment form below.
We usually say it is not possible to determine the result of zero division. Sometimes we write the result as an infinite number. In my early days of math education I always wondered why we say it undefined and write as infinity in mathematical expressions. One possible reason is to assume infinity itself as an undefined number or entity. But there was another explanation.
To understand what happens when something is divided by zero, lets make some divisions. Suppose we will divide two by some numbers. If 2 is divided by 1, the result is 1. If 2 is divided by 0.5, result is 4. If 2 is divided by 1/3, a smaller number than 0.5, result is 6. This is a bigger number than 4. In this way if you continue to divide by smaller numbers, result will continue to grow as well. Therefore we can conclude that division by a number close to the smallest positive number, which is zero, will produce a result close to the biggest positive number, which is infinity in this case. We do not need to know the actual value of infinity in this case for any reason.
It is important to note when result if division is written or assumed as infinite number, total calculation becomes an approximation and better be dealt using limiting expressions of calculus.
I hope my explanation was easy to understand. I am not claiming it as flawless, though I think it is not a wrong explanation in any way. If you have anything to ask about this explanation, feel free to use the comment form below.