Euler diagram in the context of "Proper subset"

The Organization of American States (OAS or OEA; Spanish: Organización de los Estados Americanos; Portuguese: Organização dos Estados Americanos; French: Organisation des États américains) is an international organization founded on 30 April 1948 to promote cooperation among its member states within the Americas.

Headquartered in Washington, D.C., United States, the OAS is a "multilateral regional body focused on human rights, electoral oversight, social and economic development, and security in the Western Hemisphere", according to the Council on Foreign Relations. As of November 2023, 32 states in the Americas are OAS members.

The CARICOM Single Market and Economy, also known as the Caribbean Single Market and Economy (CSME), is an integrated development strategy envisioned at the 10th Meeting of the Conference of Heads of Government of the Caribbean Community (CARICOM) which took place in July 1989 in Grand Anse, Grenada. The Grand Anse Declaration had three key Features:

1. Deepening economic integration by advancing beyond a common market towards a Single Market and Economy.
2. Widening the membership and thereby expanding the economic mass of the Caribbean Community (e.g. Suriname and Haiti were admitted as full members in 1995 and 2002 respectively).
3. Progressive insertion of the region into the global trading and economic system by strengthening trading links with non-traditional partners.

A precursor to CARICOM and its CSME was the Caribbean Free Trade Agreement, formed in 1965 and dissolved in 1973.

In mathematics, a set is a collection of different things; the things are elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables, or other sets. A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton.

Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all branches of mathematics since the first half of the 20th century.

The International Astronomical Union (IAU) adopted in August 2006 the definition made by Uruguayan astronomers Julio Ángel Fernández and Gonzalo Tancredi that stated, that in the Solar System, a planet is a celestial body that:

1. is in orbit around the Sun,
2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape), and
3. has "cleared the neighbourhood" around its orbit.

A non-satellite body fulfilling only the first two of these criteria (such as Pluto, which had hitherto been considered a planet) is classified as a dwarf planet. According to the IAU, "planets and dwarf planets are two distinct classes of objects" – in other words, "dwarf planets" are not planets. A non-satellite body fulfilling only the first criterion is termed a small Solar System body (SSSB). An alternate proposal included dwarf planets as a subcategory of planets, but IAU members voted against this proposal. The decision was a controversial one, and has drawn both support and criticism from astronomers.

A small Solar System body (SSSB) is an object in the Solar System that is neither a planet, a dwarf planet, nor a natural satellite. The term was first defined in 2006 by the International Astronomical Union (IAU) as follows: "All other objects, except satellites, orbiting the Sun shall be referred to collectively as 'Small Solar System Bodies'".

This encompasses all comets and all minor planets other than those that are dwarf planets. Thus SSSBs are: the comets; the classical asteroids, with the exception of the dwarf planet Ceres; the trojans; and the centaurs and trans-Neptunian objects, with the exception of the dwarf planets Pluto, Haumea, Makemake, Quaoar, Orcus, Sedna, Gonggong and Eris and others that may turn out to be dwarf planets.

In linguistics, the comparative method is a technique for studying the development of languages by performing a feature-by-feature comparison of two or more languages with common descent from a shared ancestor and then extrapolating backwards to infer the properties of that ancestor. The comparative method may be contrasted with the method of internal reconstruction in which the internal development of a single language is inferred by the analysis of features within that language. Ordinarily, both methods are used together to reconstruct prehistoric phases of languages; to fill in gaps in the historical record of a language; to discover the development of phonological, morphological and other linguistic systems and to confirm or to refute hypothesised relationships between languages.

The comparative method emerged in the early 19th century with the birth of Indo-European studies, then took a definite scientific approach with the works of the Neogrammarians in the late 19th–early 20th century. Key contributions were made by the Danish scholars Rasmus Rask (1787–1832) and Karl Verner (1846–1896), and the German scholar Jacob Grimm (1785–1863). The first linguist to offer reconstructed forms from a proto-language was August Schleicher (1821–1868) in his Compendium der vergleichenden Grammatik der indogermanischen Sprachen, originally published in 1861. Here is Schleicher's explanation of why he offered reconstructed forms:

In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B. The relationship of one set being a subset of another is called inclusion (or sometimes containment). A is a subset of B may also be expressed as B includes (or contains) A or A is included (or contained) in B. A k-subset is a subset with k elements.

When quantified, ${\displaystyle A\subseteq B}$ is represented as ${\displaystyle \forall x\left(x\in A\Rightarrow x\in B\right).}$