# What is 1 divided by 0?

Sep 13, 2015

Operation of dividing by $0$ is undefined, which means that the question has no answer.

#### Explanation:

Operation of division is DEFINED as follows:
Real number $C$ is called a result of division of real number $A$ by real number $B$ if and only if $B \cdot C = A$.

Assume, $B = 0$.

If $A$ is non-zero, there is no such real number $C$ that, if multiplied by $B = 0$, gives non-zero $A$ since the result of multiplication by $0$ is always $0$.
Therefore, for non-zero $A$ division by $0$ cannot be defined. The question "What is 1 divided by 0?" has no answer.

But even if $A = 0$, the situation is not much better since any number $C$ would fit the requirement of the answer to produce $0$ if multiplied by $B = 0$. Since there are infinite number of equivalent answer, the question "What is 0 divided by 0?" cannot be answered in mathematically precise form.

The above considerations led to the following statement:
DIVISION by ZERO is UNDEFINED among real numbers.
Any attempt to bring some sense into the question about the result of the division by zero is futile and is just an exercise in vanity.