[baddox]

The limit in 1b is 1 from below as well, right? I'm not sure how limits work with complex numbers, but the imaginary part of x^x approaches zero as x approaches zero from below, so can we say that the limit of x^x as x approaches zero from below is also zero?

[dllthomas]

Yes, but getting there steps out of the realm of "intuition" for me.

[baddox]

Yes, perhaps "intuition" isn't the best word. Formal limits certainly aren't "intuitive" to me, at least by one definition of the word. I suppose I used "intuitive" to mean "according to my mathematical understanding, ignoring the mathematics explicitly dealing with 0^0."

[dllthomas]

Sure. I was limiting it to things I could do in my head in tens of seconds.