A conceptual doubt in limits

Question

Why isn't $1^{\infty}$ considered as equal to $1$ but is said to be an indeterminate form in limits?

Answer 1

I think the following will clear your major doubt.

$(a)^{b} =1 $ when $a=1$ and $b \to \infty$

But ,

$(a)^{b} $ when $a \to 1$ and $b \to \infty$ can attain any (positive) value.

(By $\to 1$ , I mean a real number that tends closer and closer to $a$ but $\neq 1$.)