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Is 1/0 Undefined or Infinity?

The 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.
Is 1/0 is undefined or infinity
i. 1/0 =?
ii. 0/0 =?
iii. 1/∞ =?
  iv. ∞/ ∞ = ?

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.

i. Something/0

When we will divide something by 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 the 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. Math lovers should also read the difference between rational and irrational numbers.

Its reason is that infinity itself is not a number. It is the length of a number. When we divide a number by 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 the question that ‘Is 1/0 infinity’, you can answer in ‘No’.

ii. 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.

iii. 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 by 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 closer 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.

   i. 1/0 = Undefined

ii. 0/0 = Infinity

iii. 1/∞ = Zero (0)

iv. ∞/ ∞ = Infinity

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