After 6 years I still don't understand this

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


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

well, what I meant by neither, is that someone is not allowed to say "it's definitely 1" or "it's definitely 0". Bad wording on my part.

Also, using limits says nothing about the actual value at 0. So the limit way doesn't help. We at least get to show that those functions tend to different values, but those functions aren't continuous at x=0... so the two limits you showed don't prove that it's undetermined... technically. Guess it's a nice way of trying to make someone realize that that is the case though.

laters~

Yay for noah