EquinumerosityIn mathematics, two sets or classes A and B are equinumerous if there exists a one-to-one correspondence (or bijection) between them, that is, if there exists a function from A to B such that for every element y of B, there is exactly one element x of A with f(x) = y. Equinumerous sets are said to have the same cardinality (number of elements). The study of cardinality is often called equinumerosity (equalness-of-number). The terms equipollence (equalness-of-strength) and equipotence (equalness-of-power) are sometimes used instead.
Dirac delta functionIn mathematical physics, the Dirac delta distribution (δ distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. The current understanding of the unit impulse is as a linear functional that maps every continuous function (e.g., ) to its value at zero of its domain (), or as the weak limit of a sequence of bump functions (e.g.
Higher-order functionIn mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as arguments (i.e. a procedural parameter, which is a parameter of a procedure that is itself a procedure), returns a function as its result. All other functions are first-order functions. In mathematics higher-order functions are also termed operators or functionals. The differential operator in calculus is a common example, since it maps a function to its derivative, also a function.
Foundations of mathematicsFoundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be vague. Foundations of mathematics can be conceived as the study of the basic mathematical concepts (set, function, geometrical figure, number, etc.
Philosophy of mathematicsThe philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. The origin of mathematics is of arguments and disagreements.
Oja's ruleOja's learning rule, or simply Oja's rule, named after Finnish computer scientist Erkki Oja, is a model of how neurons in the brain or in artificial neural networks change connection strength, or learn, over time. It is a modification of the standard Hebb's Rule (see Hebbian learning) that, through multiplicative normalization, solves all stability problems and generates an algorithm for principal components analysis. This is a computational form of an effect which is believed to happen in biological neurons.
Han dynastyThe Han dynasty (UKˈhæn, USˈhɑːn; ) was an imperial dynasty of China (202 BC – 9 AD, 25–220 AD), established by Liu Bang and ruled by the House of Liu. The dynasty was preceded by the short-lived Qin dynasty (221–207 BC) and a warring interregnum known as the ChuHan contention (206–202 BC), and it was succeeded by the Three Kingdoms period (220–280 AD). The dynasty was briefly interrupted by the Xin dynasty (9–23 AD) established by usurping regent Wang Mang, and is thus separated into two periods—the Western Han (202 BC – 9 AD) and the Eastern Han (25–220 AD).
Han ChineseThe Han Chinese or Han people are an East Asian ethnic group native to China. They are the world's largest ethnic group, making up about 18% of the global population. Han Chinese people comprise various subgroups speaking distinctive varieties of the Chinese languages. The estimated 1.4 billion Han Chinese people worldwide are primarily concentrated in the People's Republic of China (including Mainland China, Hong Kong, and Macau), where they make up about 92% of the total population.
Emperor Gaozu of HanEmperor Gaozu of Han (Liu Bang; 256 – 1 June 195 BC), courtesy name Ji (季), was the founder and first emperor of the Han dynasty, reigning 202–195 BC. His temple name was "Taizu" while his posthumous name was Emperor Gao, or Gaodi; "Gaozu of Han", derived from the Records of the Grand Historian, is the common way of referring to this sovereign even though he was not accorded the temple name "Gaozu", which literally means "High Founder". Liu Bang was one of the few dynasty founders in Chinese history who was born into a peasant family.
Style (form of address)A style of office or form of address, also called manner of address, is an official or legally recognized form of address for a person or other entity (such as a government or company), and may often be used in conjunction with a personal title. A style, by tradition or law, precedes a reference to a person who holds a post or political office, and is sometimes used to refer to the office itself. An honorific can also be awarded to an individual in a personal capacity.
PrinceA prince is a male ruler (ranked below a king, grand prince, and grand duke) or a male member of a monarch's or former monarch's family. Prince is also a title of nobility (often highest), often hereditary, in some European states. The female equivalent is a princess. The English word derives, via the French word prince, from the Latin noun prīnceps, from primus (first) and caput (head), meaning "the first, foremost, the chief, most distinguished, noble ruler, prince".
QuizA quiz is a form of game or mind sport in which players attempt to answer questions correctly on one or several specific topics. Quizzes can be used as a brief assessment in education and similar fields to measure growth in knowledge, abilities, and skills, or simply as a hobby. They can also be televised for entertainment purposes, often in a game show format. The earliest known examples of the word date back to 1780; its etymology is unknown, but it may have originated in student slang.
