After 6 years I still don't understand this

x^y

y = 0

y = 4 - 4

x^(4 - 4) = x^4 / x^4 = 1 :O

That is actually the proof that x^0 = 1 for all nonzero x. Well, apart from saying that y = z - z.

0 ^ 0 isn't defined as zero nor 1. It's indeterminant. There's no question about that. Some want it to be zero, some want it to be 1. It's neither one at the moment. It's like asking what 1/0 is.

Well, actually, there are several issues by saying that it is neither one, as it would make more sense to say that it is both, mainly depending on whether you work with discrete or continuous values. I think it is a funny think to play around with, though. First of all, we know from calculus that



- right? So, set n = 1:



So, the derivative of x is usually considered to be equal to 1 for all values of x. In order to make that happen, x^0 needs to be 1.

However, according to limits, we know that



and that



so by this step, we know that it is undetermined, and we can stop the non-believers into thinking it is something else by proof!

Noah