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# Def/Minimal element

Definition of Minimal element: Suppose that $(X, \leq)$ is a poset. A minimal element of $X$ is an element $m \in S$, such that: $$\forall x \in X, m \leq x.$$

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Partial order

The following statements and definitions logically rely on the material of this page: Def/Subfield, and Def/Well ordered

To visualize the logical connections between this definition and other items of mathematical knowledge, you can visit any of the following clusters, and click the "Visualize" tab: Clust/Ordered sets