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In [[mathematics]], a '''lattice''' is a partially ordered set (also called a ''poset'') in which subsets of any ''two elements'' have a unique supremum (the elements' least upper bound; called their '''|join''') and an infimum (greatest lower bound; called their '''meet'''). Lattices can also be characterized as algebraic [[structure]]s satisfying certain axiomatic |identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These "lattice-like" structures all admit order-theoretic as well as algebraic descriptions.[http://en.wikipedia.org/wiki/Lattice_(order)]

In [[mathematics]], a '''lattice''' is a partially ordered set (also called a ''poset'') in which subsets of any ''two elements'' have a unique supremum (the elements' least upper bound; called their '''|join''') and an infimum (greatest lower bound; called their '''meet'''). Lattices can also be characterized as algebraic [[structure]]s satisfying certain axiomatic |identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These "lattice-like" structures all admit order-theoretic as well as algebraic descriptions.[https://en.wikipedia.org/wiki/Lattice_(order)]

It can readily be seen that both of these example concepts satisfy the formal definitions below

It can readily be seen that both of these example concepts satisfy the formal definitions below

The full set of concepts for these objects and attributes is shown in the illustration. It includes a concept for each of the original attributes: the composite numbers, square numbers, even numbers, odd numbers, and prime numbers. Additionally it includes concepts for the even composite numbers, composite square numbers (that is, all square numbers except 1), even composite squares, odd squares, odd composite squares, even primes, and odd primes.[http://en.wikipedia.org/wiki/Concept_lattice]

The full set of concepts for these objects and attributes is shown in the illustration. It includes a concept for each of the original attributes: the composite numbers, square numbers, even numbers, odd numbers, and prime numbers. Additionally it includes concepts for the even composite numbers, composite square numbers (that is, all square numbers except 1), even composite squares, odd squares, odd composite squares, even primes, and odd primes.[https://en.wikipedia.org/wiki/Concept_lattice]

[[Category: Mathematics]]

[[Category: Mathematics]]