We know that on an idempptent semiring $R$, the natural order relation is defined as: for all $x, y\in R$, $x\leq y$ when $x+y=y$, which is clearly a partial order relation. I am unable to point out whether this relation is a total order relation too? i.e., does it satisfy Comparability (trichotomy law)?
2026-04-03 19:37:35.1775245055
Is the natural order on an idempotent semiring total/linear?
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