Definition:Inclusion Ordered Set

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Definition

Let $\struct {S, \preceq}$ be an ordered set.


$\struct {S, \preceq}$ is inclusion ordered set if and only if:

$\mathord\preceq = \mathord\subseteq \cap \paren {S \times S}$


That means:

$\forall x, y \in S: x \preceq y \iff x \subseteq y$


Sources