I know that $0^0$ is undefined as a limit form in analysis but what about $0^{+^{0^+}}$? Isn't it equal to 1?
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8Why? $\lim_{n\to\infty}(2^{-n})^{1/n}=\frac12$. – José Carlos Santos Feb 05 '22 at 14:54
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thanks for that clarification – CHOSM Feb 05 '22 at 14:57
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3As I like to say, limits are about the journey, not the destination. In the context of indeterminant forms, limits are about the race. In the case of $0^0$, what you get depends upon how fast each element approaches zero. – Blue Feb 05 '22 at 14:59
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2You need to make up your mind if you are interested in $\lim_{(x,y)\to (0,0)\x,y>0}x^y$ or in $\lim_{x\to 0+}x^x$. The former does not exist. The latter is $1$. – Feb 05 '22 at 15:00