: For a detailed presentation of the various points of view around the definition of " algorithm " see Algorithm characterizations.

For Lie algebras the definition is slightly different.

For planets, comets and asteroids a different definition of absolute magnitude is used which is more meaningful for nonstellar objects.

For example, one definition of bandwidth could be the range of frequencies beyond which the frequency function is zero.

For a rigorous treatment of the Dirac inner product of non-normalizable states see the definition given by D. Carfì in and.

For a rigorous definition of basis with a continuous set of indices and consequently for a rigorous definition of position and momentum basis see.

For example, they might interpret a tomato as a vegetable — according to the English definition of tomato — even though the ideal Blissymbol of vegetable was restricted by Bliss to just vegetables growing underground.

For example, in Virginia, the definition of the conduct that constitutes the crime of robbery exists only in the common law, and the robbery statute only sets the punishment.

For example, jīngjì ( 经济 ／ 經濟, keizai ), which in the original Chinese meant " the workings of the state ", was narrowed to " economy " in Japanese ; this narrowed definition was then re-imported into Chinese.

For alternative ( equivalent ) formulations of the definition in terms of a bijective function or a surjective function, see the section Formal definition and properties below.

In his preface to Jürgen Osterhammel's Colonialism: A Theoretical Overview, Roger Tignor says, " For Osterhammel, the essence of colonialism is the existence of colonies, which are by definition governed differently from other territories such as protectorates or informal spheres of influence.

For example, in formal languages like mathematics, a ' stipulative ' definition guides a specific discussion.

For this reason, Locking adds that a definition of a term must not comprise of terms which are synonymous with it.

For terms such as these it is not possible and indeed not necessary to state a definition ; rather, one simply comes to understand the use of the term.

For the mathematical definition, see Decimal representation.

For square matrices with entries in a non-commutative ring, for instance the quaternions, there is no unique definition for the determinant, and no definition that has all the usual properties of determinants over commutative rings.

For example, should animal experimentation become illegal in a society, it will no longer be an ethical issue on Hoy's definition.

For example, the statement " A society is free if and only if liberty is maximized and people are required to take responsibility for their actions " is true or paradoxical, depending on the individual's definition of liberty.

For a long time this definition was used with a derogatory intention.

For all intents and purposes, the 1947 ICC definition confirmed the 1895 MCC definition and gave it international recognition and usage.

For a planar graph, the crossing number is zero by definition.

It is indeed true, as stated in the famous novel of our day, `` For Whom The Bell Tolls '', that `` no man is an island, entirely of itself ; ;

For according to them, there were seven islands in that sea in their time, sacred to Persephone, and also three others of enormous size, one of which was sacred to Hades, another to Ammon, and another one between them to Poseidon, the extent of which was a thousand stadia ; and the inhabitants of it — they add — preserved the remembrance from their ancestors of the immeasurably large island of Atlantis which had really existed there and which for many ages had reigned over all islands in the Atlantic sea and which itself had like-wise been sacred to Poseidon.

For it was here you started to go down the island, in summer.

For a return trip to Tahiti the navigators could use Sirius, the zenith star of that island.

For nearly 200 years, this remote area of the island has been called " Money Cove ".

For example, the French Rosiers family moved to the island in 1860, but subsequently abandoned it.

For 20 years, the two powers struggled for supremacy in the western Mediterranean Sea, primarily on the Mediterranean island of Sicily and its surrounding waters but also to a lesser extent in the Apennine peninsula and North Africa.

For the culture and history of the island, see article Gotland.

For a brief period in the 1790s the British attempted to establish a rival foothold on an offshore island, at Bolama, but by the 19th century the Portuguese were sufficiently secure in Bissau to regard the neighbouring coastline as their own special territory.

For a time, Leclerc met with some success ; he also brought the eastern part of the island of Hispaniola under the direct control of France in accordance with the terms of the 1795 Treaties of Bâle with Spain.

For much of the history of Roman Britain, a large number of soldiers were garrisoned on the island.

For three weeks he lived among the Typee natives, who were called cannibals by the two other tribal groups on the island — though they treated Melville very well.

For some time, scientists doubted if there could be any activity in the Beerenberg volcano, but in 1970 the volcano erupted, and added another of land mass to the island during the three to four weeks it lasted.

For the following twenty-one years, Jarvis was commercially mined for guano, sent to the United States as fertilizer, but the island was abruptly abandoned in 1879, leaving behind about a dozen buildings and 8, 000 tonnes of mined guano.

For much of the subsequent period, the main island chain, the Gilbert Islands, was ruled as part of the British Empire.

For the first few months there were next to no recreation facilities on the island, and the men amused themselves by shooting at sharks that swam into the lagoon.

For those who live on the island, it is the scene of an exile which has to be endured somehow or other ".

For example, the 12th century copperplates found at Isdhoo Island state that the monks ( Sangumanun ) from the monastery at that island were brought to Male ' and beheaded.

For the purpose, Van der Stel brought 105 Malagasy slaves to the island.

For a small island of 1 865 km < sup > 2 </ sup >, there are 2 066 km of roads in Mauritius, of which 48. 5 % are main roads, 28. 7 % are secondary roads, 3. 6 % are motorways and the remaining 19. 2 % are made up

For the next couple of centuries the island was known as Savage Island, until its original name Niu ē, which translates as " behold the coconut ", regained use.

For example, in 1901, on Goaribari Island in the Gulf of Papua, a missionary, Harry Dauncey, found 10, 000 skulls in the island ’ s Long Houses.

For several centuries, the British have used the island as a place of exile, most notably for Napoleon Bonaparte, Dinuzulu kaCetshwayo and over 5, 000 Boer prisoners.

For the next 20 years, many could find only low-paid work with the island government and the only available employment overseas for the islanders was restricted to the Falkland Islands and Ascension Island, a period during which the island was often referred to as the “ South Atlantic Alcatraz ”.