Axiom of choiceIn mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty sets is non-empty. Informally put, the axiom of choice says that given any collection of sets, each containing at least one element, it is possible to construct a new set by arbitrarily choosing one element from each set, even if the collection is infinite. Formally, it states that for every indexed family of nonempty sets, there exists an indexed set such that for every .
Zermelo–Fraenkel set theoryIn set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.
Axiom of countable choiceThe axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of non-empty sets must have a choice function. That is, given a function A with domain N (where N denotes the set of natural numbers) such that A(n) is a non-empty set for every n ∈ N, there exists a function f with domain N such that f(n) ∈ A(n) for every n ∈ N. The axiom of countable choice (ACω) is strictly weaker than the axiom of dependent choice (DC), which in turn is weaker than the axiom of choice (AC).
Axiom of global choiceIn mathematics, specifically in class theories, the axiom of global choice is a stronger variant of the axiom of choice that applies to proper classes of sets as well as sets of sets. Informally it states that one can simultaneously choose an element from every non-empty set. The axiom of global choice states that there is a global choice function τ, meaning a function such that for every non-empty set z, τ(z) is an element of z.
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.
EntrepreneurshipEntrepreneurship is the creation or extraction of economic value. With this definition, entrepreneurship is viewed as change, generally entailing risk beyond what is normally encountered in starting a business, which may include other values than simply economic ones. An entrepreneur is an individual who creates and/or invests in one or more businesses, bearing most of the risks and enjoying most of the rewards. The process of setting up a business is known as "entrepreneurship".
InnovationInnovation is the practical implementation of ideas that result in the introduction of new goods or services or improvement in offering goods or services. ISO TC 279 in the standard ISO 56000:2020 defines innovation as "a new or changed entity realizing or redistributing value". Others have different definitions; a common element in the definitions is a focus on newness, improvement, and spread of ideas or technologies.
Startup companyA startup or start-up is a company or project undertaken by an entrepreneur to seek, develop, and validate a scalable business model. While entrepreneurship includes all new businesses, including self-employment and businesses that do not intend to go public, startups are new businesses that intend to grow large beyond the solo founder. At the beginning, startups face high uncertainty and have high rates of failure, but a minority of them do go on to become successful and influential.
École polytechniqueÉcole polytechnique, also known as Polytechnique or l'X liks, is a grande école located in Palaiseau, France. It specializes in science and engineering and is a founding member of the Polytechnic Institute of Paris. The school was founded in 1794 by mathematician Gaspard Monge during the French Revolution and was militarized under Napoleon I in 1804. It is still supervised by the French Ministry of Armed Forces. Originally located in the Latin Quarter in central Paris, the institution moved to Palaiseau in 1976, in the Paris-Saclay technology cluster.
Market (economics)In economics, a market is a composition of systems, institutions, procedures, social relations or infrastructures whereby parties engage in exchange. While parties may exchange goods and services by barter, most markets rely on sellers offering their goods or services (including labour power) to buyers in exchange for money. It can be said that a market is the process by which the prices of goods and services are established. Markets facilitate trade and enable the distribution and allocation of resources in a society.
Capital marketA capital market is a financial market in which long-term debt (over a year) or equity-backed securities are bought and sold, in contrast to a money market where short-term debt is bought and sold. Capital markets channel the wealth of savers to those who can put it to long-term productive use, such as companies or governments making long-term investments. Financial regulators like Securities and Exchange Board of India (SEBI), Bank of England (BoE) and the U.S.
Grande écoleA grande école (ɡʁɑ̃d ekɔl; great school) is a specialized top level educational institution in France. Grandes écoles are part of an alternative educational system that operates alongside the mainstream French public university system and are dedicated to teaching, research and professional training in single academic fields such as engineering, architecture, business administration, academic research, or public policy and administration.
Financial marketA financial market is a market in which people trade financial securities and derivatives at low transaction costs. Some of the securities include stocks and bonds, raw materials and precious metals, which are known in the financial markets as commodities. The term "market" is sometimes used for what are more strictly exchanges, organizations that facilitate the trade in financial securities, e.g., a stock exchange or commodity exchange.
Market analysisA market analysis studies the attractiveness and the dynamics of a special market within a special industry. It is part of the industry analysis and thus in turn of the global environmental analysis. Through all of these analyses the strengths, weaknesses, opportunities and threats (SWOT) of a company can be identified. Finally, with the help of a SWOT analysis, adequate business strategies of a company will be defined.
Market economyA market economy is an economic system in which the decisions regarding investment, production and distribution to the consumers are guided by the price signals created by the forces of supply and demand. The major characteristic of a market economy is the existence of factor markets that play a dominant role in the allocation of capital and the factors of production.
Public choicePublic choice, or public choice theory, is "the use of economic tools to deal with traditional problems of political science". Its content includes the study of political behavior. In political science, it is the subset of positive political theory that studies self-interested agents (voters, politicians, bureaucrats) and their interactions, which can be represented in a number of ways – using (for example) standard constrained utility maximization, game theory, or decision theory.
Target marketA target market, also known as serviceable obtainable market (SOM), is a group of customers within a business's serviceable available market at which a business aims its marketing efforts and resources. A target market is a subset of the total market for a product or service. The target market typically consists of consumers who exhibit similar characteristics (such as age, location, income or lifestyle) and are considered most likely to buy a business's market offerings or are likely to be the most profitable segments for the business to service by OCHOM Once the target market(s) have been identified, the business will normally tailor the marketing mix (4 Ps) with the needs and expectations of the target in mind.
Market structureMarket structure, in economics, depicts how firms are differentiated and categorised based on the types of goods they sell (homogeneous/heterogeneous) and how their operations are affected by external factors and elements. Market structure makes it easier to understand the characteristics of diverse markets. The main body of the market is composed of suppliers and demanders. Both parties are equal and indispensable. The market structure determines the price formation method of the market.
Factor marketIn economics, a factor market is a market where factors of production are bought and sold. Factor markets allocate factors of production, including land, labour and capital, and distribute income to the owners of productive resources, such as wages, rents, etc. Firms buy productive resources in return for making factor payments at factor prices. The interaction between product and factor markets involves the principle of derived demand. A firm’s factors of production are gotten from its economic activities of supplying goods or services to another market.
BusinessBusiness is the practice of making one's living or making money by producing or buying and selling products (such as goods and services). It is also "any activity or enterprise entered into for profit." Having a business name does not separate the business entity from the owner, which means that the owner of the business is responsible and liable for debts incurred by the business. If the business acquires debts, the creditors can go after the owner's personal possessions.
