Subset in the context of "Meet (mathematics)"

Hypernymy and hyponymy are the semantic relations between a generic term (hypernym) and a more specific term (hyponym). The hypernym is also called a supertype, umbrella term, or blanket term. The hyponym names a subtype of the hypernym. The semantic field of the hyponym is included within that of the hypernym. For example, "pigeon", "crow", and "hen" are all hyponyms of "bird" and "animal"; "bird" and "animal" are both hypernyms of "pigeon", "crow", and "hen".

An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set of all integers is often denoted by the boldface Z or blackboard bold ${\displaystyle \mathbb {Z} }$.

The set of natural numbers ${\displaystyle \mathbb {N} }$ is a subset of ${\displaystyle \mathbb {Z} }$, which in turn is a subset of the set of all rational numbers ${\displaystyle \mathbb {Q} }$, itself a subset of the real numbers ⁠${\displaystyle \mathbb {R} }$⁠. Like the set of natural numbers, the set of integers ${\displaystyle \mathbb {Z} }$ is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, ⁠5+1/2⁠, 5/4, and the square root of 2 are not.

In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose domain is the set of positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their definition the requirement that an arithmetical function "expresses some arithmetical property of n". There is a larger class of number-theoretic functions that do not fit this definition, for example, the prime-counting functions. This article provides links to functions of both classes.

An example of an arithmetic function is the divisor function whose value at a positive integer n is equal to the number of divisors of n.

A firearm is any type of gun that shoots projectiles using high explosive pressure generated from combustion (deflagration) of chemical propellant, most often black powder in antique firearms and smokeless powder in modern firearms. Small arms is a subset of light firearms that is designed to be readily carried and operated by an individual. The term "firearm" is however variably defined in both technically and legally in different countries (see legal definitions), and can be used colloquially (sometimes incorrectly) to refer to any type of guns.

The first firearms originated in 10th-century Song dynasty China (see gunpowder weapons in the Song dynasty), when bamboo tubes containing gunpowder and pellet projectiles were mounted on spears to make the portable fire lance, which was operable by a single person and was later used effectively as a shock weapon in the siege of De'an in 1132. In the 13th century, fire lance barrels were replaced with metal tubes and transformed into the metal-barreled hand cannon, and the technology gradually spread throughout Eurasia during the 14th century. Older firearms typically used black powder as a propellant, but modern firearms use smokeless powder or other explosive propellants. Most modern firearms (with the notable exception of smoothbore shotguns) have rifled barrels to impart a stabilizing spin to the bullet for improved external ballistics.

A majority is more than half of a total; however, the term is commonly used with other meanings, as explained in the "Related terms" section below.

It is a subset of a set consisting of more than half of the set's elements. For example, if a group consists of 31 individuals, a majority would be 16 or more individuals, while having 15 or fewer individuals would not constitute a majority.

In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space).

For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails (assuming that the coin is fair). More commonly, probability distributions are used to compare the relative occurrence of many different random values.

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has 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 power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the 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.

In mathematics, a space is a set (sometimes known as a universe) endowed with a structure defining the relationships among the elements of the set.A subspace is a subset of the parent space which retains the same structure.While modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself.

A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. The nature of the points can vary widely: for example, the points can represent numbers, functions on another space, or subspaces of another space. It is the relationships that define the nature of the space. More precisely, isomorphic spaces are considered identical, where an isomorphism between two spaces is a one-to-one correspondence between their points that preserves the relationships. For example, the relationships between the points of a three-dimensional Euclidean space are uniquely determined by Euclid's axioms, and all three-dimensional Euclidean spaces are considered identical.