Venetian nobilityNobility of Italy The Venetian patriciate (Patriziato veneziano, Patrisiato venesian) was one of the three social bodies into which the society of the Republic of Venice was divided, together with citizens and foreigners. Patrizio was the noble title of the members of the aristocracy ruling the city of Venice and the Republic. The title was abbreviated, in front of the name, by the initials N.H. (Nobilis Homo or Nobiluomo), together with the feminine variant N.D. (Nobilis Domina).
ContractA contract is an agreement that specifies certain legally enforceable rights and obligations pertaining to two or more mutually agreeing parties. A contract typically involves the transfer of goods, services, money, or a promise to transfer any of those at a future date. In the event of a breach of contract, the injured party may seek judicial remedies such as damages or rescission. A binding agreement between actors in international law is known as a treaty.
Early modern periodThe early modern period of modern history spans the period after the Late Middle Ages of the post-classical era (1400–1500) to the beginning of the Age of Revolutions (1800). Although the chronological limits of this period are open to debate, the timeframe is variously demarcated by historians as beginning with the fall of Constantinople in 1453, the Renaissance period in Europe and Timurid Central Asia, the end of the Crusades, the Age of Discovery (especially the voyages of Christopher Columbus beginning in 1492 but also Vasco da Gama's discovery of the sea route to India in 1498), and ending around the French Revolution in 1789, or Napoleon's rise to power.
Early modern EuropeEarly modern Europe, also referred to as the post-medieval period, is the period of European history between the end of the Middle Ages and the beginning of the Industrial Revolution, roughly the late 15th century to the late 18th century. Historians variously mark the beginning of the early modern period with the invention of moveable type printing in the 1450s, the Fall of Constantinople and end of the Hundred Years’ War in 1453, the end of the Wars of the Roses in 1485, the beginning of the High Renaissance in Italy in the 1490s, the end of the Reconquista and subsequent voyages of Christopher Columbus to the Americas in 1492, or the start of the Protestant Reformation in 1517.
VeniceVenice (ˈvɛnᵻs ; Venezia veˈnɛttsja; Venesia veˈnɛsja, outdatedly Venexia veˈnɛzja) is a city in northeastern Italy and the capital of the Veneto region. It is built on a group of 118 small islands that are separated by expanses of open water and by canals; portions of the city are linked by over 400 bridges. The islands are in the shallow Venetian Lagoon, an enclosed bay lying between the mouths of the Po and the Piave rivers (more exactly between the Brenta and the Sile).
Group actionIn mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group acts on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it.
Set theorySet theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.
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.
ApprenticeshipApprenticeship is a system for training a new generation of practitioners of a trade or profession with on-the-job training and often some accompanying study (classroom work and reading). Apprenticeships can also enable practitioners to gain a license to practice in a regulated occupation. Most of their training is done while working for an employer who helps the apprentices learn their trade or profession, in exchange for their continued labor for an agreed period after they have achieved measurable competencies.
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".
