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Add to FavoritesMathematics is based on some models which are logically developed and are proved to be true. Number system 1-9 and 0 and their inter relationship is also a tested model which henceforth has proved all other physical and practical running models. Mathematics is based on some axioms. In our known mathematical concept division of any non-zero number by 0 gives the result infinity'.
Now let us try to interpret the physical concept of zero (0) . 0 stands for nothing' if it is alone. If it is placed at right side of a number it denotes 10's place. If we divide 10 by 2 we get 5. It means 10 units are distributed among two parts or sections .
The general equation says X/Y=Z X0 , Y0 and Z0
So , X=Y*Z
If Y tends to decrease i.e. X is distributed among more and more smaller sections then Z tends to grow bigger i.e. in each section more entity is deposited. If Y is infinitesimally small then Z is infinitely large but not more than X .
But in reality we see that 6 / 2 = 3 ( 3 < 6) but 6 / 0.5 = 12 ( 12 > 6)
So distributing a non zero entity in smaller sections may result in higher accumulation of that entity in the sections .
Visibly this is true until Y=0.
When Y=0 , physically we can say if X is distributed among nothing' segments then it remains un-fragmented i.e. unchanged. .
So we can say , at this point X=Z
But if we put this value we get X/Y=Z
So, X/Y=X
So, X/X=Y
So, 1/1=Y=1
But we have said Y=0 .
So in this case Y has two possible values 0 and 1. But Y can not have two values at a point of time.
It is not possible in our present accepted model of mathematics. It is like a un-natural zone . Until Y not = 0 all calculations follow known mathematical rules but when Y =0 the known world changes to a new kind of unnatural zone. In this zone algorithm and logic should be different .
Let us now try to interpret the above phenomenon in present logic.
From the above statement it comes out that M / 0 = M / 1
We can say that when a nonzero entity is distributed among nothing' sections it remains unchanged and at the same time when a nonzero entity is distributed among the one unit section it remains unchanged. When 100 is distributed among nothing' it gives 100 . When 100 is distributed in one part it again gives 100.
On the other hand Zero' can not only be interpreted as Nothing'.
When 0 is placed at the left of 1 gives 01, which means 1 but when 0 is placed at the right side of 1 gives 10, which means ten.
So each placement of 0 gives 10 times shift. 10 means (1+9) i.e. sum of the two extreme ends of decimal number system.
Now say 0 can be written as F(0) = (1+9)*m (1+9)*n , where m=n
F(0) = 9*(m-n)+1*(m-n)
In the above case m and n are two factors of unit.
The equation F(0) = (1+9)*m (1+9)*n says that 0 is the difference of sum of the two extreme digits of decimal number system in two different scales i.e. m and n .
From it 3 cases may arise,
(1) m =n So two scales are same and the difference F(0) is Nil .
(2) m not = n , two scales are not same and F(0) gives positive or negative value
(3) m is nearly equal to n , two scales are nearly same .
It is so can be stated that to evaluate 0 two number systems are necessary .
We can say (1 ,2,3,49 ) is one system and ( -1,-2,-3,-4,.. -9 ) is another system.
1st system is 1 , 2 , 3, 4 , 5,.9 and 2nd system is 1 i2 , 2 i2 , 3 i2 , 4 i29i2 where i2 = -1 , i is imaginary number
So difference of unit factors of two systems is (1- i2 ) = k , say = (m-n)
So the above equation becomes F(0)=9*k+1*k = 10*k = 10(1- i2 ) . So Zero function originally indicates the total number of digits in the system multiplied by the difference of the unit factors of two systems inherent in that number system.
So if a non-zero number is divided by Zero function it becomes Z = X / F(0)
Z = X / 10(1- i2 )
In this simplified form we can say that division by zero can produce a perceptible entity in some system .
Here I can not restrict myself to discuss another property of division. I have slightly discussed it before .
In the equation X/Y=Z , X and Z should not be the same entity when Y is smaller than the unit factor of that number system .
Division is a filter that changes the basic property of Number in some cases.
Suppose 6 / 2 = 3 here ( 3 < 6) i.e. 6 entities when are distributed among 2 sections accumulates 3 entities in each section .
But in the case 6 / 0.5 = 12 ( 12 > 6) . So 6 entities when are distributed among each half of the unit (i.e. 1/2 = 0.5)accumulates 12 in each section of 0.5 .How is it possible physically ?
Here 0.5 is smaller than the unit factor 1 of decimal number system . It is a relative visualization. Here 12 is the visual effect of division. In calculation we always put ourselves at the unit position. Here 12 is not of the same entity but it is practically 6 visualized from another perspective.
We can cite an example. Suppose there is a vertical pole of 20 ft height. A Man (6 ft) and an Ant (1/50th of an inch.) comes to see the pole . To the Man the pole seems higher. The Ant in his own perception of length will see the pole and the pole will seem to him gigantic.The Ant will also measure the pole in his ft-inch scale but his scale is small as per his unit of measurement. So result of division is practically the visual effect from the view point of divisor. In the same line of thinking we can say that if that ant sees a Whale , it will seem to him infinitely big and immeasurable.
It can be stated that in the systems such as in Electrical systems where two same parameters with phase difference exist , there may come some situations when some entity is divided by 0 . But we have not so far developed such appliances which can record or show that result . In practical world we are working with that algorithm on that singular incidence.
It may be the situation that if we want to know the state of the universe just before the Big Bang' that Zero function algorithm may be used .
Learn more about this author, Subhajit Basu.
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Yes
In true physical terms division by zero is not possible. It is not possible to divide any finite divisible object or material by nothing, which is what the zero denotes.
Consider division along with the other basic arithmetical operations. Let us consider that we have 10 units of some material which can be divisible in whole or in fractions. We can add 5 units more of the same and have a total of 15 units of the material. This is physically possible. We can also subtract 5 units of the material and reduce the quantity to 5 units. Similarly we can increase the physical quantity by adding multiples of 10 units to the quantity. This is multiplying. Multiplying by 1 is like leaving the original quantity untouched. You then still have 10 units of the material no change. But as you multiply by a fraction of one, which in effect is division, the quantity keeps decreasing as the fraction decreases. You keep decreasing the fraction infinitesimally (in effect dividing by a larger number) till you approach the zero level. At that point the material left is also zero. Hence multiplying by zero gives a result which is zero. In physical terms it means there is no material left.
Finally we consider division of the material. The material can be divided into two, three or any number of parts and get a physical result. Dividing by one means keeping the same number of material. There is no physical division. Dividing by a fraction in reality is a challenge as it actually means multiplication and the total increases. As a matter of deduction, division by a number greater than one gives a result which is less than the number divided. When divided by one the number divided remains unchanged. Therefore, if divided by a number lesser than one (in effect multiplying by a number greater than one) the result will be a number greater than the number divided. Thus as the denominator decreases the result keeps increasing and as the denominator becomes infinitesimally small the result gets infinitesimally large. Thus the result of dividing any number by zero is mathematically written as infinity. In actual physical terms this is not a possibility.
It however remains a mathematical concept and it has its very significant use in mathematics and science. Mathematicians do not like to come to conclusions that something is impossible. Anything looking impossible to others has some meaning in mathematics. Mathematicians have addressed the fact that zero can somehow end up in the denominator of mathematical calculations in almost every field of science. They have worked out that the result of any division with zero in the denominator is infinity. Another example of mathematically addressing an impossibility is the square root of a negative number. It gives rise to another important subject in mathematics imaginary numbers.
So the fact is that in science many a time zero does end up in the denominator giving a result called infinity, which can also be negative if the numerator is a negative number. This gives rise to the matter of interpreting what infinity (positive and negative) represents in different contexts and derive a meaning which is logical and true.
A simple example here can be the equation for optical lenses showing the relationship between the object distance, image distance and the focal distance. As the object is moved closer to the focal point of the lens the distance of the image keeps increasing as per the equation. When the object is at the focal point the object distance is equal to the focal distance. This results in a zero in the denominator of the formula for the image distance. As a result the answer for the image distance is infinity. This is interpreted that the image is being formed at an infinitely far distance from the lens meaning no image is being formed.
Thus, in science there are many occasions when the zero ends up in the denominator giving a result plus or minus infinity. This is then open to interpretation as required in the subject under study. But in a real physical terms division by zero is not possible as it does not yield a tangible result.
Learn more about this author, Rajiv Mahajan.
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