Informally it solves the following problem: Given an integer N, find its prime factors.

Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin.

** Informally, any GPS navigation device, especially an automotive navigation system

Informally, and primarily in fiction, a detective is any licensed or unlicensed person who solves crimes, including historical crimes, or looks into records.

Informally, the term is often applied in a joking manner to describe any horse that acts up and bucks with or without a rider.

Informally, if P is any polyhedron or polytope, and tP is the polytope formed by expanding P by a factor of t in each dimension, then L ( int P, t ) is the number of integer lattice points in tP.

Informally, any sloping line is called diagonal.

Informally, software developers may also use zeroise to mean any overwriting of sensitive data, not necessarily of a cryptographic nature.

Informally, a thick object in our space is simply connected if it consists of one piece and does not have any " holes " that pass all the way through it.

Informally, it states that " A random variable that depends in a Lipschitz way on many independent variables ( but not too much on any of them ) is essentially constant ".

: 4: Informally, any whaler of any size or any vessel engaged in whale watching.

Informally put, the idea behind the proof of the no-trade theorem is that if there is common knowledge about the structure of a market, then any bid or offer ( i. e. attempt to initiate a trade ) will reveal the bidder's private knowledge and will be incorporated into market prices even before anyone accepts the bid or offer, so no profit will result.

Informally, it says that any " nice looking " shape without holes can be smoothly deformed into a disk.

Informally, a Euclidean plane isometry is any way of transforming the plane without " deforming " it.

Informally, this means that whenever we are given the unit ball of some seminorm, we can find a " much smaller " unit ball of another seminorm inside it, or that any neighborhood of 0 contains a " much smaller " neighborhood.

* In 27 BC, following his defeat of Mark Antony and Cleopatra, the Roman Senate voted him new titles, officially becoming Imperator Caesar Divi Filius Augustus.

The following 139 titles of Alexis's plays have been preserved:

However, following bad sales of Dark Void and Bionic Commando, the company's management has decided to limit outsourcing to sequels and newer versions of installments in existing franchises, reserving the development of original titles for its in-house teams.

Near the end of the first decade of the double-Bills ' guidance, the Cubs won the NL pennant in 1929 and then achieved the unusual feat of winning a pennant every three years, following up the 1929 flag with league titles in 1932, 1935, and 1938.

Dozens of new first-person shooter titles appeared following Doom release, and they were often referred to as Doom " clones " rather than " first-person shooters ".

The following day, 14 September, the Senate confirmed Domitian's powers, granting tribunician power, the office of Pontifex Maximus, and the titles of Augustus, and Pater Patriae.

On May 8, 2005, a new logo was unveiled, debuting on DC titles in June 2005 with DC Special: The Return of Donna Troy # 1 and the rest of the titles the following week.

The following titles of Afranius's plays have come down to us:

He led the Dolphins to five division titles, 10 playoff appearances, and Super Bowl XIX before retiring following the 1999 season.

Tolkien: Master of Middle-earth ," which describes the impact Tolkien's writings had on him, is featured in the following titles:

Manga and anime labeled as " shōjo " need not interest only young girls, and some titles gain a following outside the traditional audience.

Other titles following in the wake of the fighting game renaissance include Persona 4 Arena, Tekken Tag Tournament 2, Soulcalibur V, and crossover titles such as PlayStation All-Stars Battle Royale and Tekken X Street Fighter.

While a comprehensive list will show the variety of titles, the following games are notable for the reasons indicated:

In addition to Prime Minister, titles used for the democratic model, where there is an elected legislative body checking the Head of government, include the following.

Such titles include the following:

A new Fighting Fantasy title, Eye of the Dragon ( by Ian Livingstone ) was released by Wizard Books in 2005, with reprints of original titles commencing the following year.

The Gieh ir-Repubblika Act, promulgated the following year, abolished all titles of nobility in Malta and mandated that they not be further recognized.

" The 11th Hour ", Psyche's 11th album, contains the following titles: " Bloodcurse ", " Yearning ", " Defenseless ", " 15 Minutes ", " September Moon ", " Until ", " The Belonging Kind ", " Justice And Damnation ", " 11th Hour ", " Buried Alive ", " Theme 7 ", and " Assassin Reprise ".

Etymologically, we can discern the following traditions ( some languages followed a historical link, e. g. within the Holy Roman Empire, not their language family ; some even fail to follow the same logic for certain other aristocratic titles ):

Although they missed the postseason in his first year with the team, they earned three division titles ( one in the first half of the strike shortened 1981 season ), two World Series appearances and their first ever World Series title () in the following four years.

Before this, Huang ( 皇 ) and Di ( 帝 ) were given as titles of a number of rulers from the era known as the " sage kings " period, supposedly predating written history, but probably coinciding with or following the invention and early stages of evolution for the Chinese writing system.

He lost his world light heavyweight title and his European heavyweight and light heavyweight titles the following year, on September 24, 1922, in a controversial bout with Senegalese fighter Battling Siki.

The longlist is announced in October or November of each year, and the shortlist ( up to 10 titles ) is announced in March or April of the year following.

In 746, Carloman ended an uprising by summarily executing all Alemannic nobility at the blood court at Cannstatt, and for the following century, Alemannia was ruled by Frankish dukes.

With the death of Theodore in 898, Sergius, with a small following of Roman nobility led by his father Benedictus, attempted to have himself elected pope, contrary to the wishes of the emperor Lambert, who was also duke of Spoleto.

Meanwhile, the Norman nobility gathered at Le Neubourg to discuss declaring Theobald king, probably following the news that Stephen was gathering support in England.

He was succeeded by his nephew Tvrtko who, following a prolonged struggle with nobility and inter-family strife, gained full control of the country in 1367.

The following year the patrons of Steinway included the Prince of Wales and other members of the monarchy and nobility.

In the following century, despite the growth of the community of Annonay, an increasing polarisation between the upper nobility families auch as Rohan Soubise, and Vogue, Count of Aubenas, possessing huge financial fortunes, and the lesser nobility, the village clergy and the bourgeoisie of the Vivarais paralleled developments elsewhere in France.

Meanwhile, the Norman nobility gathered at Le Neubourg to discuss declaring Theobald king, probably following the news that Stephen was gathering support in England.

Napoleon never gave a title of nobility to any of his commanders, as was customary following a great victory.

When the order of succession to the title is not specified in the nobility title creation charter, the following rules apply:

On 25 June 1947, De Nicola resigned from the post, citing health reasons, but the Constituent Assembly immediately re-elected him again the following day, having recognized in his act signs of nobility and humility.

At the following Estates Assembly, from 1828 to 1830, he was a representative of the nobility and also served as a law clerk.

However, following the new Instrument of Government from 1809, a change was made more in line with the British system so that, for later nobility, only the head of the family would be part of hold the title ( if there is one ).

The following titled families of high nobility are included in Kalender öfver i Sverige lefvande ointroducerad adel ( 1886 – 1899 ), Sveriges ointroducerade adels kalender ( 1912 – 1944 ), and / or Kalender över Ointroducerad adels förening ( 1935 –), which are directories of the living ( at the time of publication ) unintroduced noble families resident in Sweden.

# French refugees, who were former members of the nobility, Catholic royalist sympathizers, or anti-republicans, who were expelled by the Decree of 17 December 1791 and the Law of Suspects of 1793, following the French Revolution ;

The nobility of pre-Conquest England was ranked according to the heriot they paid in the following descending order: earl, king's thegn, median thegn.

However, under the feudal system that evolved in England following the Norman Conquest of 1066, the laws of the Crown could not have been upheld without the support of the nobility and the clergy.

Probably following Władysław's advices, in 1374 King Louis I published an earthly privilege for the nobility in Koszyce, which ensured the succession of the King's daughters after his death.

Small raids by haidamakas against Polish nobility continued in the following years under the leadership of Hnat Holy.

On December 12, 1408, following the Battle of Dobor in which he slaughtered most of Bosnia's nobility, many of whom had fought the Turks ; Sigismund and his queen, Barbara of Celje, founded the league known today as the Order of the Dragon.

The Lithuanian nobility was historically a legally privileged class in the Grand Duchy of Lithuania consisting of Lithuanians, from the historical regions of Lithuania Proper and Samogitia, and, following Lithuania's eastern expansion, many Ruthenian noble families ( boyars ).

During following centuries Lithuanian nobility began to merge into Polish nobility.

After the reform movement of the Prussian Army following a series of disastrous defeats at the hands of her enemies in the 18th century, internal analysis of the lessons learned had informed Prussian civilian and military leadership that, while individual soldiers were first rate, command structures, staff organisation and generalship was a hit-and-miss affair, more dependent on the martial skills of the King and the individual members of the German nobility who dominated the military profession.