Separable extensionIn field theory, a branch of algebra, an algebraic field extension is called a separable extension if for every , the minimal polynomial of over F is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field). There is also a more general definition that applies when E is not necessarily algebraic over F. An extension that is not separable is said to be inseparable.
SocietyA society ( səˈsaɪəti) is a group of individuals involved in persistent social interaction or a large social group sharing the same spatial or social territory, typically subject to the same political authority and dominant cultural expectations. Societies are characterized by patterns of relationships (social relations) between individuals who share a distinctive culture and institutions; a given society may be described as the sum total of such relationships among its constituent members.
WealthWealth is the abundance of valuable financial assets or physical possessions which can be converted into a form that can be used for transactions. This includes the core meaning as held in the originating Old English word weal, which is from an Indo-European word stem. The modern concept of wealth is of significance in all areas of economics, and clearly so for growth economics and development economics, yet the meaning of wealth is context-dependent. A person possessing a substantial net worth is known as wealthy.
New FoundationsIn mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled "New Foundations for Mathematical Logic"; hence the name. Much of this entry discusses NF with urelements (NFU), an important variant of NF due to Jensen and clarified by Holmes. In 1940 and in a revision in 1951, Quine introduced an extension of NF sometimes called "Mathematical Logic" or "ML", that included proper classes as well as sets.
Counterfactual historyCounterfactual history (also virtual history) is a form of historiography that attempts to answer the What if? questions that arise from counterfactual conditions. As a method of intellectual enquiry, counterfactual history explores history and historical incidents by extrapolating a timeline in which key historical events either did not occur or had an outcome different from the actual historical outcome. Counterfactual history seeks by "conjecturing on what did not happen, or what might have happened, in order to understand what did happen.
Wealth taxA wealth tax (also called a capital tax or equity tax) is a tax on an entity's holdings of assets or an entity's net worth. This includes the total value of personal assets, including cash, bank deposits, real estate, assets in insurance and pension plans, ownership of unincorporated businesses, financial securities, and personal trusts (a one-off levy on wealth is a capital levy). Typically, wealth taxation often involves the exclusion of an individual's liabilities, such as mortgages and other debts, from their total assets.
Practical reasonIn philosophy, practical reason is the use of reason to decide how to act. It contrasts with theoretical reason, often called speculative reason, the use of reason to decide what to follow. For example, agents use practical reason to decide whether to build a telescope, but theoretical reason to decide which of two theories of light and optics is the best. Practical reason is understood by most philosophers as determining a plan of action. Thomistic ethics defines the first principle of practical reason as "good is to be done and pursued, and evil is to be avoided.
Principle of sufficient reasonThe principle of sufficient reason states that everything must have a reason or a cause. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz, with many antecedents, and was further used and developed by Arthur Schopenhauer and Sir William Hamilton, 9th Baronet. The modern formulation of the principle is usually ascribed to early Enlightenment philosopher Gottfried Leibniz. Leibniz formulated it, but was not an originator.
AutodidacticismAutodidacticism (also autodidactism) or self-education (also self-learning and self-teaching) is education without the guidance of masters (such as teachers and professors) or institutions (such as schools). Generally, autodidacts are individuals who choose the subject they will study, their studying material, and the studying rhythm and time. Autodidacts may or may not have formal education, and their study may be either a complement or an alternative to formal education. Many notable contributions have been made by autodidacts.
The Wealth of NationsAn Inquiry into the Nature and Causes of the Wealth of Nations, generally referred to by its shortened title The Wealth of Nations, is the magnum opus of the Scottish economist and moral philosopher Adam Smith (1723-1790). First published in 1776, the book offers one of the world's first connected accounts of what builds nations' wealth, and has become a fundamental work in classical economics. Reflecting upon economics at the beginning of the Industrial Revolution, Smith addresses topics such as the division of labour, productivity, and free markets.
