Is 0 to the Power of 0 Undefined or Equal to 1?

[aeiti]

I was just playing with the concept of 0⁰ being undefined, and I came up with a couple of reasons. Would the steps taken in the attached image be considered correct in saying that 0⁰ is undefined in that it can be either 0 or 1 depending on how you use/define 0⁰? If they are incorrect, could someone please explain how so?

 

[Millennial]

It can be a whole bunch of other stuff, not just 0 and 1.

 

[aeiti]

Could you show me an example or point me to one?

 

[JJacquelin]

Could you show me an example or point me to one?

Hi ! There are several examples in the paper "Zero to the Zero-th Power" : http://www.scribd.com/JJacquelin/documents