Well-founded relationIn mathematics, a binary relation R is called well-founded (or wellfounded or foundational) on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is, an element m ∈ S not related by s R m (for instance, "s is not smaller than m") for any s ∈ S. In other words, a relation is well founded if Some authors include an extra condition that R is set-like, i.e., that the elements less than any given element form a set.
PovertyPoverty is a state or condition in which one lacks the financial resources and essentials for a certain standard of living. Poverty can have diverse social, economic, and political causes and effects. When evaluating poverty in statistics or economics there are two main measures: absolute poverty compares income against the amount needed to meet basic personal needs, such as food, clothing, and shelter; relative poverty measures when a person cannot meet a minimum level of living standards, compared to others in the same time and place.
MonasticismMonasticism (from Ancient Greek μοναχός, monakhos, from μόνος, monos, 'alone'), also referred to as monachism, or monkhood, is a religious way of life in which one renounces worldly pursuits to devote oneself fully to spiritual work. Monastic life plays an important role in many Christian churches, especially in the Catholic, Orthodox and Anglican traditions as well as in other faiths such as Buddhism, Hinduism and Jainism. In other religions, monasticism is criticized and not practiced, as in Islam and Zoroastrianism, or plays a marginal role, as in modern Judaism.
France in the Middle AgesThe Kingdom of France in the Middle Ages (roughly, from the 10th century to the middle of the 15th century) was marked by the fragmentation of the Carolingian Empire and West Francia (843–987); the expansion of royal control by the House of Capet (987–1328), including their struggles with the virtually independent principalities (duchies and counties, such as the Norman and Angevin regions), and the creation and extension of administrative/state control (notably under Philip II Augustus and Louis IX) in the
Australasian realmThe Australasian realm is a biogeographic realm that is coincident with, but not (by some definitions) the same as, the geographical region of Australasia. The realm includes Australia, the island of New Guinea (comprising Papua New Guinea and the Indonesian province of Papua), and the eastern part of the Indonesian archipelago, including the island of Sulawesi, the Moluccas (the Indonesian provinces of Maluku and North Maluku), and the islands of Lombok, Sumbawa, Sumba, Flores, and Timor, often known as the Lesser Sundas.
Education in AustraliaEducation in Australia encompasses the sectors of early childhood education (preschool) and primary education (primary schools), followed by secondary education (high schools), and finally tertiary education, which includes higher education (universities and other higher education providers) and vocational education (registered training organisations). Regulation and funding of education is primarily the responsibility of the States and territories; however, the Australian Government also plays a funding role.
Problem of two emperorsThe problem of two emperors or two-emperors problem (deriving from the German term Zweikaiserproblem, πρόβλημα δύο αυτοκρατόρων) is the historiographical term for the historical contradiction between the idea of the universal empire, that there was only ever one true emperor at any one given time, and the truth that there were often multiple individuals who claimed the position simultaneously.
Indomalayan realmThe Indomalayan realm is one of the eight biogeographic realms. It extends across most of South and Southeast Asia and into the southern parts of East Asia. Also called the Oriental realm by biogeographers, Indomalaya spreads all over the Indian subcontinent and Southeast Asia to lowland southern China, and through Indonesia as far as Sumatra, Java, Bali, and Borneo, east of which lies the Wallace line, the realm boundary named after Alfred Russel Wallace which separates Indomalaya from Australasia.
Pedagogy of the OppressedPedagogy of the Oppressed (Pedagogia do Oprimido) is a book by Brazilian educator Paulo Freire, written in Portuguese between 1967 and 1968, but published first in Spanish in 1968. An English translation was published in 1970, with the Portuguese original being published in 1972 in Portugal, and then again in Brazil in 1974. The book is considered one of the foundational texts of critical pedagogy, and proposes a pedagogy with a new relationship between teacher, student, and society.
Non-well-founded set theoryNon-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation. The study of non-well-founded sets was initiated by Dmitry Mirimanoff in a series of papers between 1917 and 1920, in which he formulated the distinction between well-founded and non-well-founded sets; he did not regard well-foundedness as an axiom.
