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Let $M_1$ and $M_2$ be two sets with partial order relations $\leq_1, \leq_2$ respectively. Define the sum $+$ as \[ M_1 + M_2 = M_1 \cup M_2 \] with a new order relation $\leq$ defined as * for $a,b \in M_1$, $a\leq b$ iff $a\leq_1 b$ * for $a,b \in M_2$, $a\leq b$ iff $a\leq_2 b$ * for $a\in M_1$, $b\in M_2$, $a\leq b$
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Tue, 29 May 2018 21:38 GMT