Division by Zero is not possible by any accepted definition. Let’s look at how we divide. Suppose you have a pie and you want to divide that pie by the number of people that want the pie. So, you cut the pie into four equal pieces. That way each person gets an equal share of the pie. Each person will get one fourth of the pie.
We have one pie, and four people. We use the 1 to represent the pie and four to represent the number of people or as written in mathematics, . Now, if we have something other than a pie, let us say three candy bars, and we have four people and we want each to get an equal share. Then mathematically we represent that by writing so we can see that each person gets three pieces of a candy bar if everybody gets an equal share.
There are those that say a number divided by zero is infinity. Let’s go back to a pie. Suppose we have one pie and nobody wants a piece. Mathematically we can represent that by writing 1/0. Are we going to say that everybody gets an infinite number of pieces? Of course not!
You can represent division by saying:
If A = 4 x B; then A = B + B + B + B and A B B B B = 0;
Or A/4 = B
Therefore if A = 5, B = 0 and C is unknown can we say A = B x C?
No, it defies the givens in the original problem.
That also means that A/B = C cannot be solved.
This establishes the relation between multiplication and division as defined in our world of numbers. It is a basic part of algebra. Multiplication and division can be defined differently, but no one has found a useful way of doing that.
Sometimes changing the definitions of the basics in mathematics is useful. Take for example geometry. In plane geometry two parallel lines cannot cross; in spherical geometry two parallel lines can cross. Each form of geometry is useful and so are both definitions. What could be a useful definition of division that defines division by zero?
Most of mathematics is based on the physical world and the world of physics uses mathematics to solve many problems. In the world of physics the equation for kinetic energy can be written as KE = MV2 where M = mass and V = velocity; this all works very well until we find that there are some subatomic particles that have kinetic energy, but no mass. This leaves us with the quandary of finding out how, in the case of the photon, 2KE / M = V2 = C2 where C equals the speed of light and M = 0. Perhaps, in this case we need to redefine division, but Dr. Einstein had a solution to this problem in his theory of relativity; or was Niels Bohr with quantum mechanics? It is amazing that they did all this without dividing by zero.
