# Is Division by zero Impossible – Yes

A question for all you math experts out there – is division by zero possible? On the face of it, the simple answer would seem to be no. Here’s an example: “If you have three apples and no students, how many apples will each student get?” Well, the answer of course is none. Three apples divided by zero students yields zero; no one gets an apple because there’s no one to get an apple.

This really doesn’t answer the question of whether it is possible to divide by zero, a puzzle that has occupied mathematicians for many years. Using simple arithmetic or word problems doesn’t seem to clear the matter up either. Nonetheless, let’s give it a shot to see if we can come to some kind of conclusion.

Division, if you remember basic elementary school arithmetic, is a process of repeated subtraction until you have a number left that is smaller than your divisor. For example, 4 divided by 2. That looks something like this: 4-2=2-2=0. So, in two steps of subtraction you arrive at a number less than the divisor 2, the result is 4 divided by 2 equals 2. Division by zero, however, will never yield a result smaller than zero. It is a series of subtractions that never ends. For example, let’s use the subtraction method to divide 4 by Zero and see what we get.

4 – 0 = 4 – 0 = 4 – 0 = 4, and so on to infinity ().

Let’s look at it through an algebraic equation and see what it yields us:

Let a and b be equal to non-zero and a = b. a and b = 1, qed a = b = 1.

This is obviously an illogical answer, but let’s take it one more step:

Let a and b = 1, a = b = 1

Then a2 = b, a2 – b2 = ab – b2

(a – b)(a + b) = b(a – b)

Then a + b = b, a = 0, and 1 = 0.

Again, an answer that fails the logic test as one cannot equal zero, and we’re back where we began. The inescapable conclusion is that division by zero is a logical impossibility. Until a mathematical process is invented that can figure a way out of the endless loop that results from attempts to divide by zero, this is something that we have to accept.