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Why can’t we divide by zero?

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Number System, any of various sets of symbols and therefore the rules for using them to denote numbers, which explain what percentage objects are there during a given set or in other words numeration system may be a mathematical presentation of numbers of a given set. Number systems are majorly studied in 4 types, the binary system (base 2), the decimal system which is mostly used in mathematics (base 10), the octal system (base 8), the hexadecimal system (base 16).

Whole Numbers

The whole numbers are part integers within the decimal numeration system, which include all the positive integers from 0 to infinity. These numbers exist in the number line. Hence, they are all real numbers. The complete set of natural numbers alongside ‘0’ are called whole numbers.

0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , ….∞ are whole numbers

So, ZERO (0) is a whole number. Zero is not considered a natural number but is a whole number and integer. The importance and significance of zero were once very well defined by Swami Vivekanand to the world. Let’s see the problem statement and learn why zero can not be divided, 

Why can’t we divide by zero?

When division is explained at the elementary arithmetic level, it’s often considered as splitting a group of objects into equal parts. The very reason why dividing 0 is purely undefined is because it always leads to some to the other contradiction. To begin with, how to define division? The ratio r of two numbers a and b,

r = a/b

Is that number r that satisfies

a = r × b.

Well, if b = 0, i.e., try to divide it by zero, find a number r such that

r × 0 = a × (1). But,

r × 0 = 0

For all numbers r, then unless a=0 there’s no solution of equation (1).

Now you could say that r = infinity satisfies (1). That’s a common way of putting things, but what’s infinity? It is not a number! Why not? Because if it is treated sort of a number, it will run into contradictions. Ask for instance what is obtained when adding variety to infinity. The common perception is that infinity plus any number is still infinity. If that’s so, then

Infinity = infinity +1 = infinity + 2 = infinity + 2 and so on.

Which would imply that 1 equals 2 if infinity was a number. That successively would imply that each integer is equal, for example, and the integer system would collapse.

Another example to support 

A compelling reason for not allowing division by zero is that, if it were allowed, many absurd results (i.e., fallacies) would arise. When working with numerical quantities it’s easy to work out when an illegal plan to divide by zero is being made. For example, consider the following computation.

With the assumptions,

0 × 1 = 0

0 × 2 = 0

The following is true,

0 × 1 = 0 × 2

Dividing both sides by zero gives,

(0 × 1) / 0 = (0 × 2) / 0

0 / 0 × 1 = 0 / 0 × 2

Simplified, this yields,

1 = 2

The fallacy here is that the assumption that dividing 0 by 0 may be a legitimate operation with equivalent properties as dividing by the other number.

Sample Problems

Question 1: Which of the numbers are divisible by 2: 100, 21, 35, 44, 10?

Answer:

Numbers that are even are 100, 44, and 10. Therefore, these numbers are divisible by 2.

Question 2: Which of the numbers are not divisible by 2: 122, 37, 66, 98, 97?

Answer:

Numbers 37, 97 are odd numbers. Therefore, these numbers are not divisible by 2.

Question 3: If 65,900 is divided by 0, what value will be obtained?

Answer:

If 65,900 is divided by 0, the value obtained is undefined.


Last Updated : 22 Sep, 2021
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