Definition:Lattice

Equivalence of Definitions
That the definitions above are equivalent is shown on Equivalence of Lattice Definitions.

Also defined as
Some sources refer to a bounded lattice as a lattice.

This comes down to insisting that $\vee$ and $\wedge$ admit identity elements.

Also denoted as
In particular in the context of order theory, it is common to omit $\vee$ and $\wedge$ in the notation for a lattice.

That is, one then writes $\left({S, \preceq}\right)$ in place of $\left({S, \vee, \wedge, \preceq}\right)$.

Also see

 * Bounded Lattice
 * Join Semilattice
 * Meet Semilattice
 * Semilattice (Abstract Algebra)