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."