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Is zero divided by zero equal to zero?
Answer:
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.
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.
Contributor:
Jphelm
Jphelm
First answer by M7arbles.
Last edit by Jphelm.
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