If Division by Zero Were Allowed
If Division by Zero Were Allowed
Division is a basic mathematical operation by which we divide a number called dividend by another number called the divisor. This division functions is very simple and is the base of many complex mathematical functions. But there’s a very simple division which is indefinable, and that is the division of a number by zero, which is indefinable. We have been studying through out student life that division of a number is indefinable (infinite). But still if division by zero were allowed than what kind of impacts it would have on our daily lives and surroundings?
If this were allowed it would open new breakthroughs in the realm of science, and also at the same time start many confusions and errors. The world of science and technology would be going under a serious and altering change, having deep impact on almost anything related to these fields. Impact on Mathematics: Mathematics revolves around its basic operations, addition, subtraction, multiplication and division. All complex and simple mathematical operations include the above basic operations. With out them solution would not be possible.
It has been ruled out that division of a number by zero is indefinable (infinite). By infinite we mean that it cannot be defined Let us suppose if we temporarily allow this what kind of possibilities what would we get? Let’s take a simple example in which we take the following case. Let us consider the following equations, A/B = C We can consider A = 9 B = 0 Then the above equation can be written as, 9/0 = C If we consider division by zero as possible then we can make the following changes, 9 = 0*C 9 = 0
Now from the above example we have just considered the possibility that a number can be divided by zero and taking this hypothesis we moved forward with its testing, but in the end a very baffling result is achieved: 9 = 0 This is not possible because the number 9 is something substantial and an amount which cannot be nullified in an instant. Hence this proves that whenever a there’s division by zero there will always be an anomaly, and so it can be inferred that the answer given will always be impossible. Impacts on Technology:
Our technologically advanced world is based on computer technology. The computer contains an Arithmetic Logic Unit (ALU). This unit handles all the mathematical operations performed in a computer. Even the computer programs are based on these operations. Computers can’t divide anything by zero, because they have been programmed not to do so. So if a computer were ever to divide something by zero we would be in big trouble keeping in view the original programming of the computers. Just imagine this possibility, world wide computer crashes would occur. Chaos would spread by the loss of data.
Planes, satellites, appliances would not work. Imagine what kind of life would be there. Navigational equipment might not work properly which could lead to many disasters like airplane crashes, accidents. This has happened before when On September 21, 1997, a divide by zero error in the USS Yorktown caused all the computer system on the ship to malfunction and the boat stopped in the middle of an ocean . In the present situation of our technological development, we are dependent on our computers and other such gadgets so a loss of them would be a major blow overall.
Impacts on Physics: When we study physics we may get many laws and mathematical theories in which division of a quantity with the other is made. In all these laws whenever we face a problem of division of a physical quantity with zero, we always infer it as infinite. If this zero division would be made possible the current laws would be changed as to impossible to exist in actual. We take an example of Density. Mathematically, D = m/v (Density D, mass m, volume v) We assume that volume (v) goes to zero, D = m/0 If this division is possible we can write above as,
D*0 = m This would give, 0 = m This is not possible as per Law of Conservation of Mass, which states matter can neither be created nor destroyed. Again it was seen that division by zero is ambiguous and if allowed it would lead to the impossible and impractical results. In the above stated example we clearly see that a mass can never be zero, the reason being is that a mass is weight and for it to exist it would have to have some weight and thus it is proved that it can’t be divided. Impact on Commerce and Banking:
If a bank employee or computer accidentally divides your bank balance by zero think what would happen. Wouldn’t your balance become something inexhaustible? You could use all the money available in the world and not be aware of it. Similarly in commerce, if during purchase buying of goods this mistake would occur. Either the purchaser or the seller would face bankruptcy. So the worst possible economic chaos would be occurring in the field of commerce and banking sector as only a sole party, either the bank or individual consumers, would be facing all the burden and humiliation of the bankruptcy.
University/College: University of California
Type of paper: Thesis/Dissertation Chapter
Date: 3 January 2017
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