Any Positive Number Divided By Zero Is Positive Infinity. What Is Zero Divided By Zero?
And Any Negative Number Divided By Zero Is Negative Infinity.
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."
in basic multiplication/division, anything multiplied/divided by 0 is 0
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."
Well, actually for every integers divided by zero is Undefined,
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