# Definition:Convex Set (Order Theory)/Definition 1

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## Definition

A subset $A$ of an ordered set $\struct {S, \preceq}$ is **convex (in $S$)** if and only if:

- $\forall x, y \in A: \forall z \in S: x \preceq z \preceq y \implies z \in A$

## Also see

- Results about
**convex sets**can be found**here**.

## Sources

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