In mathematics, a lattice is one of the fundamental algebraic structures used in abstract algebra. It consists of a partially ordered set in which every two elements have a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the natural numbers, partially ordered by divisibility, for which the unique supremum is the least common multiple and the unique infimum is the greatest common divisor.
Lattices can also be characterized as algebraic structures 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.
If (L, ≤) is a partially ordered set (poset), and S⊆L is an arbitrary subset, then an element u∈L is said to be an upper bound of S if s≤u for each s∈S. A set may have many upper bounds, or none at all. An upper bound u of S is said to be its least upper bound, or join, or supremum, if u≤x for each upper bound x of S. A set need not have a least upper bound, but it cannot have more than one. Dually, l∈L is said to be a lower bound of S if l≤s for each s∈S. A lower bound l of S is said to be its greatest lower bound, or meet, or infimum, if x≤l for each lower bound x of S. A set may have many lower bounds, or none at all, but can have at most one greatest lower bound.
Meet is an early Australian television series which aired on ABC during 1957. The series consisted of interviews in a 15-minute time-slot, with a single person interviewed in each episode. It aired live in Melbourne, with telerecordings (also known as kinescope recordings) made of the broadcasts so it could be shown in Sydney. In Melbourne it aired on Mondays. Following the end of the series, it was followed up with an interview series titled People.
Those who were interviewed in the series included Anona Winn,Hal Gye, Samuel Wadhams,Alan Marshall,Ian Clunies-Ross, Myra Roper,John Bechervaise, among others.
A search of the National Archives of Australia website suggests that at least two of the episodes still exist despite the wiping of the era. These episodes are the interviews with Ian Clunies-Ross and Vance Palmer.
In a partially ordered set P, the join and meet of a subset S are respectively the supremum (least upper bound) of S, denoted ⋁S, and infimum (greatest lower bound) of S, denoted ⋀S. In general, the join and meet of a subset of a partially ordered set need not exist; when they do exist, they are elements of P.
Join and meet can also be defined as a commutative, associative and idempotent partial binary operation on pairs of elements from P. If a and b are elements from P, the join is denoted as a ∨ b and the meet is denoted a ∧ b.
Join and meet are symmetric duals with respect to order inversion. The join/meet of a subset of a totally ordered set is simply its maximal/minimal element.
A partially ordered set in which all pairs have a join is a join-semilattice. Dually, a partially ordered set in which all pairs have a meet is a meet-semilattice. A partially ordered set that is both a join-semilattice and a meet-semilattice is a lattice. A lattice in which every subset, not just every pair, possesses a meet and a join is a complete lattice. It is also possible to define a partial lattice, in which not all pairs have a meet or join but the operations (when defined) satisfy certain axioms.
Cast may refer to:
An orthopedic cast, body cast, plaster cast, or surgical cast, is a shell, frequently made from plaster or fiberglass, encasing a limb (or, in some cases, large portions of the body) to stabilize and hold anatomical structures, most often a broken bone (or bones), in place until healing is confirmed. It is similar in function to a splint.
Plaster bandages consist of a cotton bandage that has been combined with plaster of paris, which hardens after it has been made wet. Plaster of Paris is calcined gypsum (roasted gypsum), ground to a fine powder by milling. When water is added, the more soluble form of calcium sulfate returns to the relatively insoluble form, and heat is produced.
The setting of unmodified plaster starts about 10 minutes after mixing and is complete in about 45 minutes; however, the cast is not fully dry for 72 hours.
Nowadays bandages of synthetic materials are often used, often knitted fiberglass bandages impregnated with polyurethane, sometimes bandages of thermoplastic. These are lighter and dry much faster than plaster bandages. However, plaster can be more easily moulded to make a snug and therefore more comfortable fit. In addition, plaster is much smoother and does not snag clothing or abrade the skin.
A cast is a basic skill on uneven bars in artistic gymnastics. From the front hang, a gymnast pikes (allowing the knee to touch the bar) and slides upwards to a handstand. Some gymnasts may perform the move with straddled legs. It is an "A" move in the Code of Points.
By willie dixon
Put it in your pocket, leave it in your shoe.
Plug it in your socket, flush it down the loo.
Hey baby, show me something new.
Put it in your hat, put it in your can.
Feed it to your cat, share it with your band.
Hey baby, help me understand.
Well they’re fighting in the kitchen and they’re fighting in the hall.
Up against the dark and up against the wall.
Why don’t you meet me in the bottom, baby; bring your running shoes.