Question

What is 1 divided by 0?

Answer 1

Hint: We need to find the value of 1 divided by 0. We start to perform a division considering number 1 as a dividend and the number 0 as a divisor. Then, we write all the cases encountered during the division to get the desired result.

Complete step by step solution:
 The division of a real number $P$ with the real number $Q$ is given as follows,
$\Rightarrow {\displaystyle \frac{P}{Q}}$
Here,
$P$ is the dividend of the division
$Q$ is the divisor of the division
Assuming the real number $R$ is the result of the above division.
Writing the expression for the same, we get,
$\Rightarrow {\displaystyle \frac{P}{Q}}=R$
Cross-multiplying the number $Q$ to the other side of the equation,
$\Rightarrow P=Q\times R$
Now,
According to our question,
Assume that the value of $Q$ is equal to 0.
$\Rightarrow Q=0$
If $P$ is the non-zero real number, there is no value of $R$ such that, if multiplied by the number $Q=0$, gives a non-zero real number $P$ since the product of any number with the number 0 is always 0.
Even if we consider the value of $P=0$ , the real number $R$ can take any number that is multiplied by $Q=0$ to give the result as the number 0.
From the above cases,
We can say that the division by the number 0 is undefined among the set of real numbers.

$\therefore$ The result of 1 divided by 0 is undefined.

Note: We must remember that the value of 1 divided by 0 is infinity only in the case of limits. The word infinity signifies the length of the number. In the case of limits, we only assume that the value of limit x tends to something and not equal to something. So, we consider it infinity. In normal cases, the value of 1 divided by 0 is undefined.