Question

The reciprocal of 0 is _?

Answer 1

Hint: We are asked to find the reciprocal of 0. We know that a number when it is multiplied by its reciprocal gives the 1. But 0, unlike any other number, when multiplied by itself gives the value as 0. It is one of the idempotent elements, that is, no matter how many times 0 is multiplied by itself, it gives the value as zero. And so, there is no number which when multiplied with zero gives the answer as 1.

Complete step-by-step solution:
According to the given question, we are asked to find the reciprocal of 0.
Reciprocal of a number can be defined as one inverse of that number such that when the number is multiplied by its inverse, we get the value of the expression as 1.
For example – we have a number say 4, the reciprocal of 4 would be \[\dfrac{1}{4}\](which is one inverse of the number we took and which is 4). Then, if we multiply the number we took by its reciprocal, we get the resultant as,
\[4\times \dfrac{1}{4}=1\], that is, we get the value as 1.
The question asked us to find the reciprocal of 0, and we know that any number when multiplied by 0 gives a value 0. Also, when 0 is multiplied by 0, it still gives the value as 0.
We can also say that, 0 is an idempotent element, that is, it gives the same result after multiplying with itself.
Since, there is no number that when multiplied with 0 gives the value 1, therefore, reciprocal of 0 does not exist.

Note: If we extend our scope and try writing the reciprocal, we will get the reciprocal of 0 as \[\dfrac{1}{0}\] which is a not defined value or an undefined value. Also, reciprocal of infinity is a perfect zero, that is, \[\dfrac{1}{\infty }=0\].