What might be meant by $\left\{0,1,2\right\}^{\mathbb{Z}}$?

Question

What might be meant by $\left\{0,1,2\right\}^{\mathbb{Z}}$?

I do not know what this notation means-

Answer 1

This is the collection of sequences $\{a_n\}_{n\in\mathbb{Z}}$ for which each term $a_n$ is one of $0$,$1$, or $2$.

Answer 2

In general $A^B$ is used to denote the set of functions $B \rightarrow A$.

Hence in your case, $$\{ 0, 1,2 \}^{\mathbb{Z}} = \{ f : \mathbb{Z} \rightarrow \{ 0, 1, 2 \} \}$$ This set can also be thought of as 'sequences' indexed by all integers (positive, zero and negative) of $0, 1$ and $2$.