In many cases such a selection can be made without invoking the axiom of choice ; this is in particular the case if the number of bins is finite, or if a selection rule is available: a distinguishing property that happens to hold for exactly one object in each bin.

The Persians found the Ionians difficult to rule, eventually settling for sponsoring a tyrant in each Ionian city.

" After a string quartet ," Martin explains, " I do not think there is a satisfactory sound for strings until one has at least three players on each line ... as a rule two stringed instruments together create a slight " beat " which does not give a smooth sound.

Due to acrylic's more flexible nature and more consistent drying time between colors, the painter does not have to follow the " fat over lean " rule of oil painting, where more medium must be applied to each layer to avoid cracking.

If the Crawford rule is in effect, then another option is the Holland rule, which stipulates that after the Crawford game, a player cannot double until after at least two rolls have been played by each side.

The consuls served for only a year ( a restriction intended to limit the amassing of power by individuals ) and could only rule when they agreed, because each consul could veto the other's decision.

The scheme functions slightly differently in each area, and is managed by each branch, but the overall rule is that each participating pub is allowed to purchase beer from whatever brewery they wish, but if it the beer is to be promoted as a ' LocAle ' it must come from a brewery within a predetermined number of miles ( which is set by each CAMRA branch, but generally is around 20 or 25 miles, although, the North London branch has set it at 30 miles ) from brewery to pub door, even if it comes from a distribution centre further away ; in addition, each participating pub must keep at least one LocAle for sale at all times.

The interaction between the two main factions is largely complementary with each faction possessing a particular expertise and both committed to the continued rule of the Communist Party and not allowing intra-party factional politics to threaten party unity.

For each rule with in its RHS, add a set of new rules consisting of the different possible combinations of replaced or not replaced with.

The 72 signatories and 166 parties to the International Covenant on Civil and Political Rights recognise this rule, under Article 14 ( 7 ): No one shall be liable to be tried or punished again for an offence for which he has already been finally convicted or acquitted in accordance with the law and penal procedure of each country.

Equivalently, the determinant can be expressed as a sum of products of entries of the matrix where each product has n terms and the coefficient of each product is − 1 or 1 or 0 according to a given rule: it is a polynomial expression of the matrix entries.

For example, we may have a rule that says each car can have only one engine associated with it ( identified by Engine Number ).

They swore that they would " in the fear and reverence of our Almighty God, mutually and severally promise amongst ourselves and each to profess and practice one truth according to that most perfect rule, the foundation whereof is ever lasting love.

Under this " Tetrarchy ", or " rule of four ", each emperor would rule over a quarter-division of the Empire.

Andrew Wheatcroft describes how some social customs such as different conceptions of dirt and cleanliness made it difficult for the religious communities to live close to each other, either under Muslim or under Christian rule.

Most scholars hold that Ezra lived during the rule of Artaxerxes I, though some have difficulties with this assumption: Nehemiah and Ezra " seem to have no knowledge of each other ; their missions do not overlap ; and no reflection of Ezra's activity appears in Jerusalem of Nehemiah.

In 325 AD Constantine I abolished the system and restored single emperor rule, but following the death of Theodosius in 395 AD, the empire returned to the system of co-emperors, each with primary authority for half the empire.

For example, just by applying a simple rule that constrains each queen to a single column ( or row ), though still considered brute force, it is possible to reduce the number of possibilities to just 16, 777, 216 ( that is, 8 < sup > 8 </ sup >) possible combinations.

Phonemes connected by a morphophonemic rule commonly show a good bit of phonetic similarity, possible because of the several dimensions of contrast in the system.

Micro-AP on the other hand covers data that show minute differences that require statistical analysis to rule out expected data that was only randomly generated.

According to Alan Ryan, the ideology of the original classical liberals argued against direct democracy, where law is made by majority vote by citizens, " for there is nothing in the bare idea of majority rule to show that majorities will always respect the rights of property or maintain rule of law.

However, he sought to win over the support of the civil population, which was necessary for his operations in Gaul and also to show his largely Germanic army the benefits of Imperial rule.

As a general rule only clergy will touch relics in order to move them or carry them in procession, however, in veneration the faithful will kiss the relic to show love and respect toward the saint.

The famous Hückel 4n + 2 rule for determining whether ring molecules composed of C = C bonds would show aromatic properties was first stated clearly by Doering in a 1951 article on tropolone.

This is not a hard-and-fast rule, however ; such mass nouns as furniture and cutlery, which represent more easily quantified objects, show that the mass / count distinction should be thought of as a property of the terms themselves, rather than as a property of their referents.

There was a bruise rule: if a prisoner had been bruised on the face, he would be shot that evening at roll call, or the next morning if the bruise first began to show then.

At first, he professed to rule only with the advice of a council formed of the nobles, but when his power became established, he dispensed with this show of republican government, and then gave himself the appearance of a legitimate title by protecting an impostor who professed to be the caliph Hisham II.

In Rome, Romulus begins to show signs of autocratic rule.

Depending on the cardroom ( or even on the particular dealer ), some rules ( such as the " show one show all " rule ) might not be enforced unless a player requests enforcement.

For example, Jean Markale's studies of Celtic societies show that the power of women was reflected not only in myth and legend but in legal codes pertaining to marriage, divorce, property ownership, and the right to rule.

This rule applies only to challenges between two successive Tribal Councils ( i. e., a typical single episode of the show ); a player can sit out a challenge immediately preceding a Tribal Council and the challenge immediately following it.

On 6 June 1947, parliamentary leader Nikola Petkov, a critic of communist rule, was arrested in the Parliament building, subjected to a show trial, found guilty of espionage, sentenced to death, and hanged on 23 September 1947.

EPA's rule requires the Department of Energy to show that Yucca Mountain can safely contain wastes, considering the effects of earthquakes, volcanic activity, climate change, and container corrosion, over one million years.

Modern historians show a kingdom that had become wealthier and more stable particularly during the first decade of his rule.

But it was Mitchel's political writings in The Nation that would show how strongly he felt with regard to English rule in Ireland.

To prove that a certain rule is customary one has to show that it is reflected in state practice and that there exists a conviction in the international community that such practice is required as a matter of law.

Furthermore, he attempted to show that even the imaginations of men are part of that same created reality, and even where misguided they cannot escape being subject to the rule of God exposed by the Christian revelation.

Though he was one of those generals who had served under Moreau, and who therefore, as a rule, disliked and despised Napoléon Bonaparte, Soult had the wisdom to show his devotion to the ruling power ; in consequence he was in August 1803 appointed to the command-in-chief of the camp of Boulogne, and in May 1804 he was made one of the first marshals of the Empire.

Unless the attorney can show that this statement falls within an exception to the hearsay rule, the factfinder ( the judge or jury ) may not consider Monica's statement ( this particular statement, however, would likely be admissible because of " Excited Utterance " and " Present sense impression " exceptions ).

The appointment of a warrior to an important post was intended to show the Emperor that the samurai class was not ready for a purely civilian rule.

The show takes place in " Future Century ", where Space Colonies have agreed that rather than having war to decide who controls everyone a fighting tournament is held every four years between the space colonies to decide the right to rule instead.