Notation 3.3.4.1. Let $Q$ be a partially ordered set. Every finite, nonempty, linearly ordered subset $S \subseteq Q$ has a largest element, which we will denote by $\mathrm{Max}(S)$. The construction $S \mapsto \mathrm{Max}(S)$ determines a nondecreasing function $\mathrm{Max}: \operatorname{Chain}[Q] \rightarrow Q$, where $\operatorname{Chain}[Q]$ is defined as in Notation 3.3.2.1.
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