), though analysis as a formal concept is a relatively recent development.

As a formal concept, the method has variously been ascribed to Alhazen, René Descartes ( Discourse on the Method ) and Galileo Galilei.

The Roman Catholic Church likewise treats it as any other act of renunciation of the Catholic faith, although for a few years, from 2006 to 2009, it did note in the baptismal register any formal act of defection from the Catholic Church, a concept quite distinct from that of presentation of such a certificate.

Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

This definition of potential, while formal, has little practical application, and a more useful concept is that of electric potential difference, and is the energy required to move a unit charge between two specified points.

The mathematical roots of the idea of fractals have been traced through a formal path of published works, starting in the 17th century with notions of recursion, then moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 21st century.

The first formal language is thought be the one used by Gottlob Frege in his Begriffsschrift ( 1879 ), literally meaning " concept writing ", and which Frege described as a " formal language of pure thought.

While formal language theory usually concerns itself with formal languages that are described by some syntactical rules, the actual definition of the concept " formal language " is only as above: a ( possibly infinite ) set of finite-length strings, no more nor less.

The notion of a formal grammar may be closer to the intuitive concept of a " language ," one described by syntactic rules.

Donald Knuth notes that Hans Peter Luhn of IBM appears to have been the first to use the concept, in a memo dated January 1953, and that Robert Morris used the term in a survey paper in CACM which elevated the term from technical jargon to formal terminology.

* The Beis Yaakov educational movement, begun in 1917, introduced the concept of formal Judaic schooling for Orthodox women.

In mathematics, logic, and formal systems, a primitive notion is an undefined concept.

This notion was an underpinning for his concept of the spiral curriculum which posited the idea that a curriculum should revisit basic ideas, building on them until the student had grasped the full formal concept.

To encourage the initiative of Red Army commanders, the CPSU temporarily abolished political commissars, reintroduced formal military ranks and decorations, and the Guards unit concept.

In addition to highlighting such formal aspects of the predicate " is true ", some deflationists point out that the concept enables us to express things that might otherwise require infinitely long sentences.

As a formal religious concept in Confucianism, Dao is the Absolute towards which the faithful move.

The concept of a formal theorem is fundamentally syntactic, in contrast to the notion of a " true proposition " in which semantics are introduced.

Hoare's most significant work has been in the following areas: his sorting algorithm ( Quicksort ), Hoare logic, the formal language Communicating Sequential Processes ( CSP ) used to specify the interactions between concurrent processes, structuring computer operating systems using the monitor concept, and the axiomatic specification of programming languages.

As a formal concept, it has appeared in jurisprudence, commerce and scholasticism long before it was given a rigorous mathematical foundation.

* Deductive closure, the application of the mathematical concept to formal logic

However, full civil equality was obtained only when they received the formal rights of citizenship, which had long been withheld from them in their own communities of Endingen and Lengnau.

Its magnificence has impressed heads of state, and it has witnessed many different types of events, from formal civil ones to record launches, fashion shows, children's Christmas parties and private functions.

Impeachment is a formal process in which an official is accused of unlawful activity, the outcome of which, depending on the country, may include the removal of that official from office as well as criminal or civil punishment.

If civil commitment proceedings follow, the evaluation is presented in a formal court hearing where testimony and other evidence may also be submitted.

In law as practiced in countries that follow the English models, a pleading is a formal written statement filed with a court by parties in a civil action, other than a motion.

Since the Empire lacked any formal means of nominating a successor, succession usually involved the death of competing princes in order to avert civil unrest and rebellions.

Due to a dearth of formal government statistics and the recent civil war, it is difficult to gauge the size or growth of the economy.

Legal systems in all socialist states preserved formal criteria of the Romano-Germanic civil law ; for this reason, law theorists in post-socialist states usually consider the Socialist law as a particular case of the Romano-Germanic civil law.

Until recently, there was no formal protection for those who spoke up from a position of knowledge inside government, with even senior civil servants ( Shiv Chopra being one notable case ) fired or constructively dismissed for speaking up about internal abuses.

Civil and political rights need not be codified to be protected, although most democracies worldwide do have formal written guarantees of civil and political rights.

Decorations and orders: Military, civil, and organizational decorations are usually worn only to full dress events, generally of formal governmental or diplomatic significance.

As part of his general policy of concessions of formal power to the German princes and ending the civil wars within the kingdom, Frederick further appeased Henry by issuing him with the Privilegium Minus, granting him unprecedented entitlements as Duke of Austria.

When civil war broke out in Pakistan in 1971, Bhutan was the first nation to recognize the new government of Bangladesh, and formal diplomatic relations were established in 1973.

The above sense of " de facto " is related to the relationship between common law traditions and formal ( statutory, regulatory, civil ) law, and common law marriages.

Most Orthodox rabbinical seminaries or yeshivas also require dedication of many years to education, but few require a formal degree from a civil education institutions that often define Christian clergy.

A formal church hierarchy was set up, parallel to the civil administration, whose areas of responsibility often coincided.

Although as in other jurisdictions a resident of Quebec may informally use whatever name he or she wants, procedures for formal name change are very strict as Quebec ( unlike the rest of Canada ) operates under a civil law system.

In particular, under the administration of Tony Blair, the influence of two Downing Street special advisers, Jonathan Powell and Alastair Campbell, both of whom were given formal power over Downing Street civil servants, provoked widespread criticism.

Some consider the World Social Forum to be a physical manifestation of global civil society, as it brings together non governmental organizations, advocacy campaigns as well as formal and informal social movements seeking international solidarity.

The pro-treaty wing of Sinn Féin had decided to formally break off and become a distinct party in late December 1922, but its formal launch was delayed until after the New Year as a direct consequence of the turmoil caused by the civil war.

It was later passed into formal law by the Long Parliament in 1641 and became one of the three constitutional documents of English civil liberties, along with the Magna Carta and the Bill of Rights 1689.

Although her father was prohibited from formal political activity because of his role as a civil servant, he became editor of the Bradford Pioneer, the city's socialist newspaper, after William Leach was elected to Parliament in the 1935 general election.

Mannerheim's great-grandfather, Count Carl Erik Mannerheim ( 1759 – 1837 ), had held a number of offices in Finland's civil service during the early years of the autonomous Russian Grand Principality of Finland, including membership in the Senate, and served as the first Prime Minister of Finland ( formally the Vice Chairman of the Economic Department of the Senate-the Senate consisted of Economic Department, later the cabinet, and the Justice Dpt, later the Supreme Court, and the formal chairman of both was the Governor General as the acting head of state ).