Division by Zero: Is it Really Possible?
My first reaction to this question is: Who cares? Don't we have more important things to worry about? My second reaction is: Somebody asked the question so let's try to answer it. The difficulty will be choosing the right words to get my thoughts into the mind of whoever reads this.
Do you remember when you were first introduced to math in school? To add one and one the teacher used apples or oranges to represent the numbers. You take one apple and put it in a basket. Now you take another apple and put it in the basket. How many apples are in the basket? None!? OOPS. My basket had a hole in it. (Sorry about that. I just can't resist a little humor.) I patched the hole and started over. Now I have two apples in the basket. This is how they were able to get the concept of math into our minds. I will try to use these same apples to divide by zero.
Let's try a simple example first. Start out with a basket of ten apples. We'll call it basket A. Next, put an empty basket next to it. We'll call this one basket B. Now, get another several baskets and put two apples in each one. Start dumping the apples from the baskets containing two apples into basket B. How many baskets containing two apples did you have to dump into basket B before it had as many apples as basket A? Five baskets. Therefore 10 divided by 2 equals 5.
Now lets divide by zero the same way. Take basket A and put one apple in it. Place empty basket B next to it. Now get a stack of baskets with no apples in them. A big stack! So big that no matter how many you have the stack's not big enough. Start dumping the empty baskets into basket B. How many would you have to dump to get basket A to equal basket B. One hundred, one million, an infinite number? No. Even if you empty an infinite number of empty baskets into basket B you will never have one apple in it like basket A has. Therefore, we can safely say that division by zero is impossible if you are dividing into a number other than zero.
However, what if we divide zero by zero? Let's try it. Eat the apple in basket A so it is empty. Make sure B is empty also. Start dumping empty baskets from the pile into basket B. How many must you dump before basket A equals basket B? One, one hundred, one million? The answer is yes to all. No matter how many empty baskets you dump into B, it will always equal A.
Conclusion. In the real world, division by zero is possible as long as you are dividing into zero and the answer can be any real number in existence. In other words, 0 (the dividend) / 0 (the devisor) = any real number (the quotient).