# Semilattice vs Lattice - What's the difference?

semilattice | lattice | Derived terms |

## As nouns the difference between semilattice and lattice

is that semilattice is (mathematics) a partially ordered set that either has a join (a least upper bound) for any nonempty finite subset (a join-semilattice'' or ''upper semilattice'') or has a meet (or greatest lower bound) for any nonempty finite subset (a ''meet-semilattice'' or ''lower semilattice ) while lattice is a flat panel constructed with widely-spaced crossed thin strips of wood or other material, commonly used as a garden trellis.

## As a verb lattice is

to make a lattice of.

# semilattice

## English

### Noun

(en noun) (wikipedia semilattice)
• (mathematics) A partially ordered set that either has a join (a least upper bound) for any nonempty finite subset (a join-semilattice'' or ''upper semilattice'') or has a meet (or greatest lower bound) for any nonempty finite subset (a ''meet-semilattice'' or ''lower semilattice ).
• # lattice

## English

(wikipedia lattice)

### Noun

(en noun)
• A flat panel constructed with widely-spaced crossed thin strips of wood or other material, commonly used as a garden trellis.
• (heraldry) A bearing with vertical and horizontal bands.
• (crystallography) a regular spacing or arrangement of geometric points, often decorated with a motif.
• (order theory) A partially ordered set in which every pair of elements has a unique supremum and an infimum.
• (group theory) A discrete subgroup of Rn which spans the real vector space Rn.
• #### Synonyms

* latticework

#### Hyponyms

* (algebra) complete lattice * (algebra) distributive lattice

#### Hypernyms

* (algebra) partially ordered set

#### Derived terms

* Boolean lattice * complete lattice * crystal lattice * distributive lattice * lattice bridge * lattice girder * lattice energy * lattice plant * lattice point * lattice window * semilattice * space lattice

* grid

### Verb

(lattic)
• To make a lattice of.
• to lattice timbers
• To close, as an opening, with latticework; to furnish with a lattice.
• to lattice a window

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