But what if you're in a context where you're not reasoning about continuous functions at all? Why would you have to be subject to reasoning that doesn't apply to your situation?
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.
