Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
Empty setIn mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set".
Muscle cellA muscle cell is also known as a myocyte when referring to either a cardiac muscle cell (cardiomyocyte) or a smooth muscle cell, as these are both small cells. A skeletal muscle cell is long and threadlike with many nuclei and is called a muscle fiber. Muscle cells (including myocytes and muscle fibers) develop from embryonic precursor cells called myoblasts. Myoblasts fuse from multinucleated skeletal muscle cells known as syncytia in a process known as myogenesis.
Joint dislocationA joint dislocation, also called luxation, occurs when there is an abnormal separation in the joint, where two or more bones meet. A partial dislocation is referred to as a subluxation. Dislocations are often caused by sudden trauma on the joint like an impact or fall. A joint dislocation can cause damage to the surrounding ligaments, tendons, muscles, and nerves. Dislocations can occur in any major joint (shoulder, knees, etc.) or minor joint (toes, fingers, etc.). The most common joint dislocation is a shoulder dislocation.
Anatomical terms of motionMotion, the process of movement, is described using specific anatomical terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relative to the anatomical position of the body parts involved. Anatomists and others use a unified set of terms to describe most of the movements, although other, more specialized terms are necessary for describing unique movements such as those of the hands, feet, and eyes.
Rough setIn computer science, a rough set, first described by Polish computer scientist Zdzisław I. Pawlak, is a formal approximation of a crisp set (i.e., conventional set) in terms of a pair of sets which give the lower and the upper approximation of the original set. In the standard version of rough set theory (Pawlak 1991), the lower- and upper-approximation sets are crisp sets, but in other variations, the approximating sets may be fuzzy sets. The following section contains an overview of the basic framework of rough set theory, as originally proposed by Zdzisław I.
Universal setIn set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, it can be proven in multiple ways that a universal set does not exist. However, some non-standard variants of set theory include a universal set. Many set theories do not allow for the existence of a universal set. There are several different arguments for its non-existence, based on different choices of axioms for set theory. In Zermelo–Fraenkel set theory, the axiom of regularity and axiom of pairing prevent any set from containing itself.
Upper limbThe upper limbs or upper extremities are the forelimbs of an upright-postured tetrapod vertebrate, extending from the scapulae and clavicles down to and including the digits, including all the musculatures and ligaments involved with the shoulder, elbow, wrist and knuckle joints. In humans, each upper limb is divided into the arm, forearm and hand, and is primarily used for climbing, lifting and manipulating objects. In formal usage, the term "arm" only refers to the structures from the shoulder to the elbow, explicitly excluding the forearm, and thus "upper limb" and "arm" are not synonymous.
Fuzzy setIn mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, defined a more general kind of structure called an L-relation, which he studied in an abstract algebraic context. Fuzzy relations, which are now used throughout fuzzy mathematics and have applications in areas such as linguistics , decision-making , and clustering , are special cases of L-relations when L is the unit interval [0, 1].
Adhesive capsulitis of the shoulderAdhesive capsulitis, also known as frozen shoulder, is a condition associated with shoulder pain and stiffness. It is a common shoulder ailment that is marked by pain and a loss of range of motion, particularly in external rotation. There is a loss of the ability to move the shoulder, both voluntarily and by others, in multiple directions. The shoulder itself, however, does not generally hurt significantly when touched. Muscle loss around the shoulder may also occur. Onset is gradual over weeks to months.
