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# Could division as a mathematical function logically mean something else?

Author: Ravinder Bhardwaj

The word ‘Division’ in mathematics is an operation that means the opposite of multiplication. The division is normally written as Numerator/Denominator or N/D in short, for example, 10/5 that would give 2 as an answer. Let us understand this with an example using some apples visible in a basket in a real-life scenario. Suppose 20 apples in a basket should be equally (in number) shared between two people which means each person would get 10 apples in their baskets. In the mathematical expression, we write this as 20/2 which would result in 10 as the answer. Suppose two more people join in for their share. Now 20 apples need to be divided among 4 people. Mathematically it can be written as 20/4 which would result in 5 as the answer that means each person would get 5 apples in their share. Likewise, if 20 apples were shared equally between 10 people then each person would get 2 apples because 20/10 gives 2 as the answer.

Now going back to the N/D form and apply it to the scenario of sharing 20 apples between people. This can be interpreted as the Denominator (D) tells the total number of parts into which the Numerator (N) should be divided equally. So, in the case of 20/4, when numerator 20 is divided equally into 4 denominator parts, the answer is 5 or 20/4 = 5. Similarly, in the case of 20/10, the numerator 20 is divided equally into 10 denominator parts and the answer is 2 or 20/10 = 2. Now put this in a simple logical argument; when the ‘Denominator’ indicates the parts into which the item in the ‘Numerator’ should be divided equally than in the scenario of only one person with 20 apples the equation can be written as 20/1 = 20. That is when 20 apples are divided between one person then the person would receive all 20 apples. Now taking this logic a bit further and let us introduce the number Zero. Zero represents null, nothing or emptiness. In mathematics, any number when is divided by 0 gives infinity (∞) or the expressions like 1/0 are considered undefined. Applying the expression in a similar scenario of 20 apples, then the division of 20 apples among zero people should result in the same number of apples in the basket, that is 20/0 = 20. In other words, the Denominator 0 tells the Numerator 20 that apples should be divided equally among 0 number of people, therefore at the end, the number of apples that remained in the basket would still be 20 - A FINITE VALUE, NOT INFINITE.