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The theory of lattices in the sense of order theory. For the number-theoretic notion, use the tag "lattices" instead.
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A complete lattice of functions
Let $D$ be a set, $\mathbb{N_0}$ the set of natural numbers including zero. Let $P$ be the set of all functions from $D$ to $\mathbb{N_0}$, i.e. $P = \lbrace m \mid m: D \rightarrow \mathbb{N_0} \rbra …