Let \(\alpha, \beta \in \mathbb{N}^n\) multi-indices. Then
\begin{equation*} \alpha\le \beta \iff\forall i\in \{1,\ldots,n\}: \alpha_i \le \beta_i. \end{equation*}Let \(\alpha, \beta \in \mathbb{N}^n\) multi-indices. Then
\begin{equation*} \alpha\le \beta \iff\forall i\in \{1,\ldots,n\}: \alpha_i \le \beta_i. \end{equation*}