Technically, division by zero is “undefined”, not impossible. In other words, no one has offered an (acceptable) definition for the possibility. As a result, for most quantitative purposes division by zero is prohibited. Calculators and math gods alike run into this foreboding barrier.
What is needed, therefore is a reason for the concept to exist; necessity is the mother of invention (as well as the language needed to quantitatively describe many inventions, mathematics.) Consider the following statement: “There are 10 kinds of people in the world: those who understand binary and those who don’t.” For virtually all purposes of business, life, love, and death there is no reason to use the binary system directly. Yet for virtually all purposes of business, life, love and death binary is extremely important. In fact, you would not be reading this article if it were not for a computer’s ability to process binary numbers!
Every commercially available computer uses a seemingly endless stream of ones and zeros which represent whether a switch is open or closed. (A computer is really nothing more than a series of switches on steroids in a manner of thinking) Only two numbers are used, hence the term binary. In the statement above, 10 is the binary equivalent of the number 2. The number 3 would be 11, the number 4 would be 100, the number 5 would be 101 and so on. Necessity is the mother of invention.
What about negative numbers? There was a time in which people believed that negative numbers, i.e. numbers less than zero were completely absurd and meaningless. Mathematicians who lived during this time would routinely disregard any calculation that resulted in a negative number as meaningless and absurd. It wasn’t until the concepts of debt and depreciation were invented that humanity embraced the concept of a value that represents less than nothing.
Ask any 5th grader what the square root of sixteen is and they should be able to tell you the answer is four. Four, however is only one possible answer as negative four time negative four is also sixteen- -4 x -4 = 16. So what then is the square root of negative sixteen? Negative four times negative four does NOT equal negative sixteen, any more than two plus two is equal to five. The answer involves something called imaginary numbers.
Imaginary numbers are used to answer the question, what is the square root of a negative number? The letter “i” (written in italics) is defined as the square root of negative one. Therefore, the square root of negative sixteen becomes 4 (the square root of 16) times “i” (defined as the square root of -1) or simply 4i. The ”i” stands for the imaginary unit ( ‘I” for imaginary; I’ll notify the press!) and was defined when there was a need for it. Today imaginary and complex numbers (numbers with imaginary and real components, such as 3 +2i or -4 -2i) are used in a variety of applications suchs as engineering, computer science and 3D graphic design.
All of this demonstrates that unless a quantity is useful in a certain way it may not be defined mathematically. It doesn’t mean the quantity cannot exist in the real world-the world where everybody but my ex-girlfriend lives. Advances in nanotechnology could be the catalyst for having the definition of division by zero defined once and for all. Ohm’s Law describes the relationship between the three components of electric circuits, voltage, current and resistance. In a super conducting circuit the voltage could be reduced to zero (yet the current would still flow) which would introduce the real possibility of dividing by zero in calculating the other two components of electricity.
Necessity is still the mother of invention. One day it will crucial to have division by zero defined. What implications and breakthroughs that will result are anyone’s guess.