Definition: Let $T$ be a tree. Given a set $X$, we define a $T-tuple$ of elements of $X$ to be a function
x: $T\rightarrow X$
Alternatively, we sometimes refer to a $T$-tuple as a tree of elements in X. If x is a $T$-tuple, we often denote the value of x at t by $x_t$. Also, the function x is denoted $(x_t)_{t\in T}.$
I am having trouble accessing the meaning of the above definition. How would the Cantor ternary construction be expressed using this language?