So, we actually had a discussion at work today about whether 0/0 is undefined or indeterminate.
One viewpoint is that you can no more discuss division by zero than you can discuss how far you can drive in your house; it's just not a valid operation over the domain.
The other viewpoint is that while 0/0 is undefined since anything divided by 0 is undefined, anything over itself is 1, and 0 over anything is zero. Since it yields to multiple values, it is indeterminate.
Yet another camp, orthogonal to the other two says division by zero is undefined, but division by a limit that goes to zero is indeterminate (that is, the value you get depends on the limits you start with).
It amuses me greatly that we are having this conversation. Two of the websites citing for the differing views are: Dividing by 0 and 0 As the Denominator.