Question

What is the value of \[\dfrac{1}{0}\]?

Answer 1

Hint: To solve this type of problem, first we need to know about zero and its property. By using this property, we will get the answer as undefined. Because there is no particular answer for this question.

Complete step by step solution:
Before, solving this question first we need to understand the concept of zero and its property
Zero is the integer that precedes the positive number one and follows the number −1. In most of the numerical systems, 0 was identified even before the idea of 'negative integers' was accepted. Zero is an integer that quantifies a count or an amount of null size; that is, if the number of your brothers is equal to zero, this means the same thing as having no brothers. Hence, zero is neither positive nor negative.
Zero has some special property \[\dfrac{a}{0}=\,\text{undefined}\] where, \[a\ne 0\] and some other properties.
Here, we will discuss the third property that is \[\dfrac{a}{0}\]. From the question we have \[a=1\]
In this problem, we have to find the value of \[\dfrac{1}{0}\].
For that we have to consider the variable r that is
\[\Rightarrow r=\dfrac{1}{0}---(1)\]
From this above equation by cross multiplying this we get:
\[\Rightarrow r.0\ne 1---(2)\]
Above equation (2) is impossible because according to the property of zero is \[a.0=0\] Which contradicts our earlier assumption that \[a\ne 0\]. What this contradiction tells us is that there is no defined form for r. So, division by zero is said to be undefined.
Hence, the value of \[\dfrac{1}{0}\] is undefined.

Note: While solving this type of problem, many of the students have misconception about the property of zero that when number is divided by zero is infinity this statement is wrong because we can see in the solution that when we multiply any number with zero then final answer will lead to zero. But when we simplify the given problem then we get the \[r.0\ne 1\]. Hence, we can say that when any number is divided by zero it is always undefined.