Operation of division is DEFINED as follows:
Real number CC is called a result of division of real number AA by real number BB if and only if B*C=AB⋅C=A.
Assume, B=0B=0.
If AA is non-zero, there is no such real number CC that, if multiplied by B=0B=0, gives non-zero AA since the result of multiplication by 00 is always 00.
Therefore, for non-zero AA division by 00 cannot be defined. The question "What is 1 divided by 0?" has no answer.
But even if A=0A=0, the situation is not much better since any number CC would fit the requirement of the answer to produce 00 if multiplied by B=0B=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.
