Division is the most important concept in mathematics. If we want to solve mathematical problems, we should have a strong grip on the division. That’s why our teachers teach us this concept during the early classes of our educational career. While learning division, we try to solve different kinds of problems. When we try to solve 1/0, we can’t get a satisfactory answer. Its reason is that 1/0 is undefined. Before knowing why 1/0 is undefined, you should look at the following examples and try to get their answers.

ü 1/0 =?

ü 0/0 =?

ü 1/∞ =?

ü ∞/ ∞ = ?

Most of the students can’t understand these terms. That’s why
these terms confuse us. Here, we will try to understand these terms. After
understanding these terms, we can easily find out the answers to these
questions;

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## Something/0

When we will divide something with zero, the answer is
undefined. The main reason behind this fact is that the value of this division
is not defined yet. Now, we have got the first part of the answer to this
question. If someone asks a question that ‘Is 1/0 undefined?’, our answer
should be ‘Yes’. Now, we move towards the second part of the question. If we
are asking that something/0 is infinity, we have to impose a limit on it.

Its reason is that
infinity itself is not a number. It is the length of a number. When we divide a
number with another number, we get its answer in the form of a number. For
example, when we divide 6/3, we get 2 and it is a number. In this case, when we
divide something with zero, we should also get a number. As infinity is not a
number. Therefore, it can’t be the answer to this question. Therefore, when
someone asks a question that ‘Is 1/0 infinity’, you can answer in ‘No’.

## 0/0 or ∞/ ∞

When we divide
zero by zero or infinity by infinity, we can’t get a properly defined answer.
That’s why the answer to this expression is indeterminate. Its reason is that
these are true mathematical expressions. We should get a proper answer to these
mathematical expressions but we are not getting the exact value. Sometimes,
there is also a possibility that we are getting the exact value but this value
is undefined. It means that we don’t know these values. We can say that these
are indeterminate terms. If we add infinity to infinity or we subtract infinity
from infinity, the answer is also infinity. Its reason is that infinity may be
a positive number or a negative number. Therefore, we can’t determine the
direction of the infinity. Similarly, if we multiply infinity with zero, its
answer is also in the indeterminate form.

## 1/∞

The answer to this expression is zero. When we divide a small
number by a large number, we get an answer that is very close to zero. For
example, when we divide 1 with 10 (1/10), the answer is 0.1. It is close to
zero. When we divide 1 by 100 (1/100), the answer is 0.01. This answer is more
close to zero. Now, if we divide 1 by 1000000 (1/1000000), the answer is
0.000001. It is even closer to zero. We can conclude that the larger the
denominator, the closer the answer to zero. That’s why we consider it zero.

ü 1/0 = Undefined

ü 0/0 = Infinity

ü 1/∞ = Zero (0)

ü ∞/ ∞ = Infinity

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