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| No | 46% | 562 votes | Total: 1212 votes | |
| Yes | 54% | 650 votes |
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Add to FavoritesIs division by zero really impossible? My computer certainly seems to think so. If I run a badly written program that tries to divide by zero, up shoots a message scolding me "You have committed a division by zero error, program terminating."
When I try to divide by zero on my calculator and I get a row of symbols that manages to convey the message, "Only dorks do this."
So, what is the problem? Consider dividing 100 by 10, the answer is 10. Divide 100 by 5, and the answer is 20. The following is true
100 / 10 = 10
100 / 1 = 100
100 / 0.1 = 1000
100 / 0.01 = 10,000
100 / 0.00001 = 10,000,000
Plot the numbers above on a piece of graph paper with divisor on the x-axis, and result on the y-axis, and you get a line which always shoots off the top of the paper when it approaches the y-axis. No matter what size the paper, no matter what scale on the y-axis the result is the same. This is called an asymptotic line.
Basically, the smaller the number used to divide, then the larger the result. If zero is used as the divisor, then the result is as large as large can be. This value is called infinity. Computers and calculators are not at all happy to see it. They have no way of representing such a number, hence the abuse.
But human beings are another matter. Mathematics is about doing the impossible and thinking the unthinkable, even if it does give you a headache.
So here is a clever thought experiment. Forget about paper for a moment and consider a sheet of glass. Hold the glass upright on a table with a strong light source behind it. Take a marker pen and draw on the glass. Any mark on the glass casts a shadow on the table.
You will notice that the nearer to the level of the source of light a mark is made, the further down the table the shadow falls. If a point is plotted at the same level as the source of light it falls an infinitely large distance down the table!
Now, put our original graph paper flat on the table in front of the upright glass. Re-plot our original data on the glass in such a way as the shadow from glass thrown matches the paper graph on the table.
Now by examining the glass, you can not only explore what happens to our equation at infinity, but can take a look at points drawn above the light, beyond infinity!
How is the headache coming?
Learn more about this author, T J Neale.
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Yes
In simple mathematics, division indicates the ratio between two numbers a' and b'. So, any number when divided by zero has been termed undefined to prevent arguments and complications. However, in complex mathematics division by zero is possible.
When, a number is multiplied with zero, it yields zero. So, if the inverse of the number is taken it comes to an undefined fraction of 0/0. This fraction has not been resolved nor argued by mathematicians since centuries.
But, let us take a case where 1 is divided by zero and an absurd number U' is the result. So, U multiplied by zero and then multiplied by two, results into two. As, U being the inverse of zero when multiplied with zero becomes 1 and 1 multiplied with two results into two, which is the law of multiplication. Thus, there lies a definition that division by zero can be possible; however the context is not with real or imaginary numbers but with an absurd number defined as U.
This argument can be further justified by the anomaly of squares and square roots. When, two negative numbers are multiplied it gives to a positive number. So, it is not possible to have a square root of a negative number. So, mathematicians had to come up with complex numbers which had imaginary number i', as a multiplication factor to the square root of the negative number. Thus, the complex number has a real and an imaginary part. The imaginary part of the rational number has its importance in practical calculations of electrical engineering.
So, how does the absurd number has its existence? Philosophically, what exists' is question that has to be defined. When, we think of love, hate or other emotions, we know it is there but there is no physical definition to these feelings. Two people can show different variations of love which cannot be defined by laws or rules. A mother and a son would love each other in a different way than the same son with his newly wed wife. Similarly, we also know that God is omnipresent but we have no physical evidence or a proof of His existence.
Sometimes it is transitional of something's existence and a possibility of the existence in a particular domain. Division of zero is not possible in a real and imaginary number system but, in absurd mathematics it is possible to divide zero and get a number. This fact is strengthened more with extended complex plane and calculus. The L'Hospital Rule in calculus also describes the functionality of division by zero within a particular limit. In extended complex plane, the factor 1/0 has been termed as complex infinity.
Finally, the concept of absurd numbers and division by zero should be limited within a particular domain of absurd numerical. In real or imaginary number system, these numbers or the concept might not find a place but in other domains it is possible.
Learn more about this author, Subhadeep Dasgupta.
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