Now suppose that for each index $\displaystyle k\in K$ there is a set $\displaystyle A_k$. In the equation

, the left-hand side is something like $\displaystyle ((\dots((A_1\cup A_2)\cup A_3)\cup\dots)\cup A_8)\cup A_9$, if $\displaystyle \cup$ is considered left-associative. The right-hand side is $\displaystyle \Big(\big((A_1\cup A_2)\cup A_3\big)\cup\big((A_4\cup A_5)\cup A_6\big)\Big)\cup \big((A_7\cup A_8)\cup A_9\big)$. The original associative law $\displaystyle (A_1\cup A_2)\cup A_3=A_1\cup(A_2\cup A_3)$ is obtained by taking $\displaystyle J_1=\{1\}$ and $\displaystyle J_2=\{2,3\}$.