If Russian pupils have to take these languages, how come American students have a choice whether or not to take a language, but have to face so many exceptions??

The statement of the axiom of choice does not specify whether the collection of nonempty sets is finite or infinite, and thus implies that every finite collection of nonempty sets has a choice function.

Because of independence, the decision whether to use of the axiom of choice ( or its negation ) in a proof cannot be made by appeal to other axioms of set theory.

Alternatively, a coin may be tossed, with the winners choosing whether to serve or receive first, or choosing which end of the court to occupy, and their opponents making the leftover the remaining choice.

The choice of stroke depends on how near the shuttlecock is to the net, whether it is above net height, and where an opponent is currently positioned: players have much better attacking options if they can reach the shuttlecock well above net height, especially if it is also close to the net.

) The one major exception to this in practice is the axiom of choice — unless studying this axiom in particular, the majority of researchers do not usually worry whether a result requires the axiom of choice.

Just as the older dictionaries it includes uniquely Canadian words and words borrowed from other languages, and surveyed spellings, such as whether colour or color was the more popular choice in common use.

Many would also find it unacceptable that an ISP, whether by law or by the ISP's own choice, should deploy such software without allowing the users to disable the filtering for their own connections.

Dissenting opinions included Justice Stevens's, who wrote "... the voluntary character of the private choice to prefer a parochial education over an education in the public school system seems to me quite irrelevant to the question whether the government's choice to pay for religious indoctrination is constitutionally permissible.

* Controversy over exact choice of rules for gun safety ( specifically whether or not " the gun is always loaded " is an intelligent rule ).

The Australian Government was merely asked, as a matter of courtesy, whether they approved of the choice or not.

These include the choice over whether to adopt a current standard, or move towards a more neutral, but artificial one.

An interesting innovation was introduced in Russia in the judicial reform of Alexander II: unlike in modern jury trials, jurors decided not only whether the defendant was guilty or not guilty, but they had the third choice: " Guilty, but not to be punished ", since Alexander II believed that justice without morality is wrong.

In some words in Hebrew there is a choice of whether to use a mater lectionis or not, and in modern printed texts matres lectionis are sometimes used even for short vowels, which is considered to be grammatically incorrect, though instances are found as far back as Talmudic times.

Also, many families had a choice of whether or not they wanted to employ a midwife who practiced the traditional folk medicine or the newer methods of professional parturition.

All the action is usually done secretly and it is an individual's choice whether to give a hint of their identity or stay anonymous.

Receiving devices have an " Omni on / off " mode that determines whether they respond to all channels or only one, and a choice of " mono " or " poly " mode, which determines whether the instrument plays monophonically or polyphonically.

The tactics room and the command helmet offer a choice of visual displays of various kinds and audio inputs, allowing the user to track individual and group movements, whether of spaceships or soldiers.

Much academic debate regarded one or both of two pragmatic topics: how ( or whether ) to apply utilitarianism to problems of political policy, or how ( or whether ) to apply economic models ( such as rational choice theory ) to political issues.

* Pro-choice, the view that women should have the choice of whether or not to terminate a pregnancy

His choice of consuls for the year 362 was more controversial.

He proposed Brutus and Collatinus as the first two consuls and that choice was ratified by the curiae.

Both courts collaborated in the choice of the yearly consuls, as each court chose a consul and accepted the other's choice.

The reasons for this choice are obscure, though Livy often cast the decision according to the class struggles he saw as endemic during this period, with patricians generally favoring consuls and plebs the military tribunes.

The Intermediates in the Class with the Judge were asked to pick 4 winners and give their reasons but their decisions did not affect the choice of the Judge.

They had been kind to us and we were indebted to them for one or two pleasant dinners, and for information as to where to shop, which dentist, doctor, plumber, and sitter to call ( not that there was much of a choice, since Catatonia was just a village ; ;

But at Yalta the conflicting expectations of East and West were merged into an agreement by the Big Three to assist all liberated countries in Europe `` to create democratic institutions of their own choice ''.

His report of life there covers a wide range of topics, such as marriage in heaven ( where all angels are married ), children in heaven ( where they are raised by angel parents ), time and space in heaven ( there are none ), the after-death awakening process in the World of Spirits ( a place halfway between Heaven and Hell and where people first wake up after death ), the allowance of a free will choice between Heaven or Hell ( as opposed to being sent to either one by God ), the eternity of Hell ( one could leave but would never want to ), and that all angels or devils were once people on earth.

The members were given a choice of either offering armed forces or paying a tax to the joint treasury ; most states chose the tax.

The Melians were offered a choice to join the Athenians, or be conquered.

Modern aestheticians have asserted that will and desire were almost dormant in aesthetic experience, yet preference and choice have seemed important aesthetics to some 20th-century thinkers.

England had no choice but to build a powerful navy if it were to regain global power.

The separation and declaration of the republics were made out of necessity rather than a personal choice.

Like Case, many cyberpunk protagonists are manipulated, placed in situations where they have little or no choice, and although they might see things through, they do not necessarily come out any further ahead than they previously were.

In all forms of thought coercion the immediate objective is to force other people to act as if their basic choice rules were identical to those of the coercing party.

At a time when history painting was considered the supreme classification for public art, Chardin's subjects of choice were viewed as minor categories.

The choice of a small islet as a home may seem odd today, yet waterways were the main channels for both communication and travel until the 19th century in much of Ireland and especially Highland Scotland.

Since the 1970 NFL-AFL merger, league rules were changed to allow the Super Bowl home team to pick their choice of jersey.

Appointments by influence were common in the navy at this time, but the significance of Beatty's choice lay in Seymour's relative inexperience as a signals officer, which later resulted in difficulties in battle.

) He has insinuated that votes were lost because of the choice of a female candidate.

For instance, New Zealand's landmark reform in 1989, during which schools were granted substantial autonomy, funding was devolved to schools, and parents were given a free choice of which school their children would attend, led to moderate improvements in most schools.

Eusebius held that men were sinners by their own free choice and not by the necessity of their natures.

His choice of subject was prophetic: with hindsight the work appears to foretell, in the most powerful terms, the disasters that were shortly to be visited upon Europe in the Second World War.

The founding of a Fifth Republic was supported by the French people, while France's colonies were given the choice between more autonomy in a new French Community and immediate independence.

B. M. Hertzog, who had recently insisted on his choice of Lord Clarendon as Governor-General of that country, and the selection of an Irishman as Governor-General of the Irish Free State – both of these appointments were agreed to despite royal disfavour.

48-215 sedans were produced in parallel with the 50-2106 coupé utility from 1951 ; the latter was known colloquially as the " ute " and became ubiquitous in Australian rural areas as the workhorse of choice.

Electors were free to vote for whomsoever they pleased ( including themselves ), but dynastic considerations played a great part in the choice.

In premodern Muslim countries, Jews rarely faced martyrdom, exile or forcible conversion, and were mostly free in their choice of residence and profession.