He could produce carefully constructed orations, set and formal speeches, artfully and prayerfully made by writing and rewriting with all the aid his tutor and others could provide, and then delivered verbatim from memory.

While there is no generally accepted formal definition of " algorithm ," an informal definition could be " a set of rules that precisely defines a sequence of operations.

That notion is central for explaining how formal systems come into being starting from a small set of axioms and rules.

This led to the first of a number of periods in which an outside power controlled Athens ; Often the outside power set up a local agent as political boss in Athens ; but when Athens was independent, it operated under its traditional form of government ; even the bosses, like Demetrius of Phalerum, kept the traditional institutions in formal existence.

Although Zermelo's fix allows a class to describe arbitrary ( possibly " large ") entities, these predicates of the meta-language may have no formal existence ( i. e., as a set ) within the theory.

Naive set theory can be seen as a stepping-stone to more formal treatments, and suffices for many purposes.

Furthermore, a firm grasp of set theoretical concepts from a naive standpoint is important as a first stage in understanding the motivation for the formal axioms of set theory.

Links in this article to specific axioms of set theory describe some of the relationships between the informal discussion here and the formal axiomatization of set theory, but no attempt is made to justify every statement on such a basis.

Gottlob Frege did explicitly axiomatize a theory in which the formalized version of naive set theory can be interpreted, and it is this formal theory which Bertrand Russell actually addressed when he presented his paradox.

A formal grammar defines ( or generates ) a formal language, which is a ( usually infinite ) set of finite-length sequences of symbols ( i. e. strings ) that may be constructed by applying production rules to another sequence of symbols which initially contains just the start symbol.

A formal statement needs some set of hypotheses which exclude these situations.

Such institutional support may include government recognition or designation ; presentation as being the " correct " form of a language in schools ; published grammars, dictionaries, and textbooks that set forth a " correct " spoken and written form ; and an extensive formal literature that employs that dialect ( prose, poetry, non-fiction, etc .).

: Foundations of Geometry ) published by Hilbert in 1899 proposes a formal set, the Hilbert's axioms, substituting the traditional axioms of Euclid.

A value expressed using an encoding scheme may thus be a token selected from a controlled vocabulary ( for example, a term from a classification system or set of subject headings ) or a string formatted in accordance with a formal notation, for example, " 2000-12-31 " as the ISO standard expression of a date.

In formal education, a curriculum is the set of courses and their content offered at a school or university.

Then the equivalence class of the pair can be identified with the rational number, and this equivalence relation and its equivalence classes can be used to give a formal definition of the set of rational numbers.

Although formal certification of his freedom from Burghley's control was deferred until May 1572, Oxford was finally granted the income of £ 666 which his father had intended him to have earlier, but properties set aside to pay his father's debts would not come his way for another decade.

Formalist film theory is a theory of film study that is focused on the formal, or technical, elements of a film: i. e., the lighting, scoring, sound and set design, use of color, shot composition, and editing.

In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols.

The alphabet of a formal language is the set of symbols, letters, or tokens from which the strings of the language may be formed ; frequently it is required to be finite.

An alphabet, in the context of formal languages, can be any set, although it often makes sense to use an alphabet in the usual sense of the word, or more generally a character set such as ASCII.

As to form, a discourse may be either a formal, or set, sermon ; a homily ; or a catechetical instruction.

After a sermon was preached a formal deed of possession was drawn up and signed by the officers and chaplains.

Presumably those who did not have a formal church connexion had also felt the influence of Christianity to a greater or lesser extent.

A similar French influence is seen in classroom ASL in francophone West Africa, where ASL was introduced along with formal education for the deaf by the deaf American missionary Andrew Foster.

However, the weight of Byzantine Imperial influence and the threat of continual Turkish raids, discouraged a formal separation of the Galatians and instead they returned to the orbit of Byzantine control.

In periods of relative liberalization, the influence of people and organizations outside the formal party structure has tended to increase, particularly in the economic realm.

The decision process inside the structure has become less and less formal, but influence of the Council has become stronger and stronger.

By then, the economic pressures of the Depression as well as the in-house pressure to reduce expenditures, and possibly the academic background of the parent body in Oxford, combined to make OUP's primary musical business that of publishing works intended for formal musical education and for music appreciation −− again the influence of broadcast and recording.

Though he had no formal students, many artists have cited him as an influence, including Willem de Kooning, Jim Dine, and Mark Rothko.

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.

" Zukofsky was a major influence on the Language poets, who carried the Imagist focus on formal concerns to a high level of development.

It follows that whoever wields personal influence and power can legitimize this only by gaining a formal position in the hierarchy, with commensurate authority.

It follows that whoever wields personal influence and power can legitimize this only by gaining a formal position in the hierarchy, with commensurate authority.

Although the term " sons of liberty " had been used in a generic fashion well before 1765, it was only around February 1766 that its influence as an organized group, using the formal name " Sons of Liberty ", extended throughout the colonies, leading to the development of a pattern for future resistance to the British that would carry the colonies towards 1776.

Notably, John Gallagher and Ronald Robinson in their 1953 article The Imperialism of Free Trade would argue that Hobson placed too much emphasis on the role of formal empire and directly ruled colonial possessions, not taking into account the significance of trading power, political influence and informal imperialism.

The monarchy has remained but the King has lost all formal political influence and is reduced to a mere symbolic head of state.

His work with translations of German and South American poets, as well as the influence of Robert Bly, had considerable influence on his own poems ; this is most evident in The Branch Will Not Break, which departs radically from the formal style of Wright's previous book, Saint Judas.

Its influence, in recent years, evolved toward a more formal role, and it came to be used primarily for official purposes such as diplomacy, politics, and other forms of official documentation.

They can be like some clubs, but much less formal .< ref > They are usually known in many countries to cause social unrest and also have negative influence on the members and may be a target for the law enforcers in case of any social vices

Among the cultural aspects of corporate visual identity management, socialization – i. e., formal and informal learning processes – turned out to influence the consistency of a corporate visual identity.

However, Tromp's death was a severe blow to the Dutch – few now expected to beat the English ; the Orangist faction lost political influence and Grand Pensionary Johan de Witt was willing to give formal treaty assurances to Cromwell that the infant William III of Orange would never become stadtholder, thus turning the Netherlands into a base for a Stuart restoration.

During the long controversy which followed the publication in 1841 of Tract 90 and which ended in the withdrawal of John Henry Newman from the Anglican Church, he used all his influence to protect from formal condemnation the leaders and tenets of the " Tractarian " party.

" Curtis had Sheridan arrested for insubordination but Halleck's influence appears to have ended any formal proceedings.

While there may be a formal alliance or other treaty obligations between the influenced and influencer, such formal arrangements are not necessary and the influence can often be more of an example of soft power.

Similarly, a formal alliance does not necessarily mean that one country lies within another's sphere of influence.