TITLE: Math interval notations: Interval raised to a power?
QUESTION [5 upvotes]: I saw this equation in a paper:
$v = (v_{l,0}, v_{r,0}, v_{l,1}, v_{r,1}, v_{l,2}, v_{r,2}, v_{l,3}, v_{r,3}) ∈ [−1, 1]^8 $
What does this interval notation mean?- $[−1, 1]^8$

REPLY [3 votes]: It is exponentiation in the context of the Cartesian product of sets. For example:
\begin{align}
[-1, 1]^3 
&= [-1, 1] \times [-1, 1] \times [-1, 1] \\
&= \{ (x_1, x_2, x_3) \mid x_1, x_2, x_3 \in [-1, 1] \}
\end{align}