Question

Find the value of reciprocal of zero.

Answer 1

Hint: The definition of reciprocal of a number is 1 divided by the number. When we multiply a number by its reciprocal, we get 1. We describe 0 as the number between the set of all negative numbers and the set of all positive numbers. We have infinity (\[\infty \]) defined as a number greater than any assignable quantity or countable number.

Complete Step-by-Step solution:
Reciprocal is what to multiply a value by to get 1 it is also known as “Multiplicative Inverse”. Generally reciprocal of a given number is written as inverse of the number.
Anything upon zero is infinity and as we have infinity defined as a number greater than any assignable quantity or countable number. So, we have infinity as a not defined number.
Therefore, anything upon zero is not defined. Same is the case with reciprocal of zero.
Writing 0 alone means we have \[\dfrac{0}{1}\].
Then the Reciprocal of 0 is given as
\[\dfrac{1}{0}=\infty \]
Or it can be written as,
\[\dfrac{1}{0}=Infinity\], which is not defined.
Hence reciprocal of 0 is infinity, i.e. it is not defined.

Note: The possibility of error in this question is putting \[\dfrac{1}{0}\] directly as “not defined” which is wrong because we have to show \[\dfrac{1}{0}\] to be equal to Infinity then only we can talk about the not defined form.