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There is one problem with defining division by zero this way. If we look at what happens as we approach zero from the negative side, then the answer becomes negative infinity, and it is positive infinity if we approach from the positive side. We would say, the limit of a/b as b approaches infinity is undefined.

Even worse, what if a is also 0?

So in the extended real number line, the expression a/0 is undefined.

Another way to look at this is the link between division and multiplication.

If a/0 = b where a and b are some real numbers and a and b are not 0, then we must have 0b=a. If a was zero then we are dealing with 0/0 which is also not a defined real number. So we say a is not 0.

0 b=0 and that means a is zero? It just doesn't work. The bottom line is

no number multiplied by zero will produce a product other than zero.

Division by zero is not defined!

Q: What is 12 divided by 0?

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