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### Best Answer nadp says

It is not really correct to say that any positive number divided by zero is infinity.

The "division algorithm" says that, for example,

8/2 = 4, because (2)(4) = 8

If we try to carry this to division by 0, then we have

8/0 = ? This makes no sense because there is no quantity that can be multiplied by 0 and produce 8. Any number multiplied by 0 would result in 0. Thus, we say that division by 0 is "undefined."

However, we can say that the "limit" of 8 divided by some number x is infinity, as x "approaches" zero.

As for zero divided by zero, we don't run into the same contradiction as when we try to divide a non-zero number by zero. But we cannot determine an answer to this division:

0/0 = ? Well, as we've already said 0 times any number is zero. So the "?" can be replaced by any number at all and we would have a true statement. Thus, we say that 0/0 is "indeterminate."

### Larry Fields says

Nadp is correct. And I'd like to explain why.

When we divide 2 by a very tiny positive number t, we get a very large positive number. Experiment with this idea on your electronic calculator.

On the other hand, if we divide 2 by a very tiny negative number -t, we get a negative number having a very large magnitude.

If we let t approach zero from the positive direction, the quotient approaches POSITIVE infinity.

On the other hand hand, if we let t approach zero from the negative direction, the quotient approaches NEGATIVE infinity.

This is too crazy to even think about; so we just say, "Division by zero is undefined."