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Actually 0/0 is undefined because there is no logical way to define it. In ordinary mathematics, you cannot divide by zero.

The limit of x/x as x approaches 0 exists and equals 1 so you might be tempted to define 0/0 to be 1.

However, the limit of x2/x as x approaches 0 is 0, and the limit of x/x2 as x approaches 0 does not exist .

r/0 where r is not 0 is also undefined. It is certainly misleading, if not incorrect to say that r/0 = infinity.

If r > 0 then the limit of r/x as x approaches 0 from the right is plus infinity which means the expression increases without bounds. However, the limit as x approaches 0 from the left is minus infinity.

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Q: Is zero divided by zero equal to zero?
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