TITLE: Is $0^\infty$ indeterminate?
QUESTION [28 upvotes]: Is a constant raised to the power of infinity indeterminate? I am just curious. Say, for instance, is $0^\infty$ indeterminate? Or is it only 1 raised to the infinity that is?

REPLY [4 votes]: Since the question came to the front page again, let's do a complex example, to show that (at least this time) Mathematica is not crazy...
For $t>0$, let $f(t) = t, g(t) = i/t$.  Then
$$
\lim_{t\to 0+} f(t) = 0,\qquad \lim_{t\to 0+}g(t) = \infty
\\
f(t)^{g(t)} = \exp\frac{i\;\log t}{t}
$$
and $\mathrm{Re} \Big(f(t)^{g(t)}\Big)$ (pictured) does not converge as $t \to 0^+$.