I need help with this notation from Wikipedia:
Suppose we have pairs $(X_1,Y_1), (X_2,Y_2), \dots, (X_n,Y_n)$ taking values in $\mathbb R^d \times \{1,2\}$.
Does it mean the following:
$X_1, X_2, \dots, X_n$ are the first elements in the pairs so they take values in the set $\mathbb R^d$. \begin{align} X_1 &\in \mathbb R^d, \quad \text{i.e.} \quad X_1=(X_{11}, X_{12}, \dots, X_{1d} ) \tag 1 \\ X_2 &\in \mathbb R^d, \quad \text{i.e.} \quad X_2=(X_{21}, X_{22}, \dots, X_{2d} ) \tag 2 \\ &\vdots \\ X_n &\in \mathbb R^d, \quad \text{i.e.} \quad X_n=(X_{n1}, X_{n2}, \dots, X_{nd} ) \tag 3 \\ \end{align} $Y_1, Y_2, \dots, Y_n$ are the second elements in the pairs so they take one value in the set $\{1,2\}$, i.e. $1$ or $2$. \begin{align} Y_1 &\in \{1,2\}, \quad \text{i.e.} \quad Y_1=1 \quad \text{or} \quad Y_1=2 \tag 4 \\ Y_2 &\in \{1,2\}, \quad \text{i.e.} \quad Y_2=1 \quad \text{or} \quad Y_2=2 \tag 5 \\ &\vdots \\ Y_n &\in \{1,2\}, \quad \text{i.e.} \quad Y_n=1 \quad \text{or} \quad Y_n=2 \tag 6 \end{align}
Is this correct?