Definition:Bottom (Lattice Theory)

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Definition

Let $\left({S, \vee, \wedge, \preceq}\right)$ be a lattice.


Definition 1

Let $S$ admit a smallest element $\bot$.


Then $\bot$ is called the bottom of $S$.


Definition 2

Let $\vee$ have an identity element $\bot$.


Then $\bot$ is called the bottom of $S$.


Equivalence of Definitions

These definitions are shown to be equivalent in Equivalence of Definitions of Bottom.


Also see