That's actually an interesting point. And actually it occurs to me that even in continuous equations you have a problem:
Does it matter if we are talking 0^x or x^0?
I would think that in the context of 0^x, you'd have a constant function of 0, but x^0 you'd have a constant function of 1. These have different limits as x -> 0.
I think you have just convinced me that 0^0 is undefined.
Edit: Ouch. 0^x can't be defined for a negative x, so that doesn't work. I am back to siding with 1.
Does it matter if we are talking 0^x or x^0?
I would think that in the context of 0^x, you'd have a constant function of 0, but x^0 you'd have a constant function of 1. These have different limits as x -> 0.
I think you have just convinced me that 0^0 is undefined.
Edit: Ouch. 0^x can't be defined for a negative x, so that doesn't work. I am back to siding with 1.