The complete phrasing of the question: Why can’t you divide a certain number by zero? Supposedly, the meaning of dividing by zero is that you do not divide the number (you “divide” it to 0 sets…) and so the result should be the same as the number divided?

Hello Yosef, dividing by zero has no meaning. The division of a number by 1 is dividing the number to one set and the result is the number of elements in the set. Obviously, dividing by zero at the same logic would not work, as even if we assume that the meaning of dividing the number by zero is dividing it to zero sets, how many elements are in these “zero sets”? Clearly, we cannot answer that question. What we can say is that when you divide a number by a very small number ‒ one that tends towards zero, the result would be a number that tends towards infinity. As infinity is not a number (the rules of infinity are different from the rules of “regular” natural numbers, for example: infinity plus infinity equals infinity) we can only say that the result approaches infinity.

The symbol of infinity.
The symbol of infinity.

This can be demonstrated in the following manner:

1/1:2 = 2

1/1:4 = 4

1/1:100 = 100

1/1:100,000 = 100,000

Therefore, we can see that the smaller the denominator the greater the result (this is not a mathematical proof, but only an example).

Why can’t you divide by zero? TED-Ed:

Dr. Yossi Elran
Davidson Institute of Science Education
Weizmann Institute of Science