Complement of Top

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Theorem

Boolean Algebra

Let $\struct {S, \vee, \wedge, \neg}$ be a Boolean algebra.


Then:

$\neg \top = \bot$


Bounded Lattice

Let $\struct {S, \vee, \wedge, \preceq}$ be a bounded lattice.


Then the top $\top$ has a unique complement, namely $\bot$, bottom.


Also see