Although originally controversial, the axiom of choice is now used without reservation by most mathematicians, and it is included in ZFC, the standard form of axiomatic set theory.

Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

( Although it was perhaps implied, he did not include an axiom requiring at least one subset to be independent.

Although it is constantly made to look foolish ( too simple to come in out of the rain, people say, who have found in the innocent an impediment ), it does not mind looking foolish because it is not concerned with how it looks.

Although he questions the extent and nature of the alleged revival of religion and the alleged increase in conformity, and thinks that `` hedonistic '' present-time orientation does not have the meaning usually attributed to it, he does conclude that Americans increasingly enjoy leisure without guilt, do not stress achievement so much as formerly, are more accepting of group harmony as a goal, more tolerant of diversity and aware of other cultures.

Although it does not follow the metrical rules for a blues to be sung, the phrases themselves carry a blues feeling.

Although the play does show a certain structural amateurishness ( there are eleven acts varying in length from twenty-five seconds to an hour and a half ), the statement it makes concerning the ceaseless yearning and searching of youth is profound and worthy of our attention.

Although this technique is simple and satisfactory, one practical difficulty does exist: the direction of true north must be known for each launch point.

Although Brooklyn College does not yet have a junior-year-abroad program, a good number of students spend summers in Europe.

Although the titan Rhea does present Dionysus with an amethyst stone to preserve the wine-drinker's sanity in historical text.

Although when burned, amber does give off a characteristic " pinewood " fragrance, modern products, such as perfume, do not normally use actual amber.

Although the terms adiabatic and isocaloric can often be interchanged, adiabatic processes may be considered a subset of isocaloric processes ; the remaining complement subset of isocaloric processes being processes where net heat transfer does not diverge regionally such as in an idealized case with mediums of infinite thermal conductivity or non-existent thermal capacity.

Although Ajax speaks earnestly and is well received, he does not succeed in convincing Achilles.

Although Asser never mentions Alfred's law code, he does say that Alfred insisted that his judges be literate, so that they could apply themselves " to the pursuit of wisdom.

Although it does not match the German exactly, Wheen's title has justly become part of the English language and is retained here with gratitude.

The Court ruled, " Although an Alford plea allows a defendant to plead guilty amid assertions of innocence, it does not require a court to accept those assertions.

Although his name does not appear in any other part of the Jewish Bible, Rabbinic tradition holds Habakkuk to be the Shunammite woman's son, who was restored to life by Elisha in 2 Kings 4: 16.

Although a dormant company, dormancy does not preclude a company actively operating as a nominee shareholder.

Although there is no proof, the name " Thomas Corbett " does appear on the list of dead and missing.

Although in 2002 the NYSE and the NASDAQ required that nominating committees consist of independent directors as a condition of listing, nomination committees have historically received input from management in their selections even when the CEO does not have a position on the board.

Although prepared for an armed conflict with Nigeria in recent years, the Cameroon Army does not have operational experience against other forces, therefore, it is not possible to assess its ability to respond to changing threats and opposing tactics.

Although technology does not exist currently to measure this, it can be estimated by determining oxygen consumption by the brain.

Although Confucius the man may have been a believer in Chinese folk religion, Confucianism as an ideology is humanistic and non-theistic, and does not involve a belief in the supernatural or in a personal god.

Although the Apocrypha was part of the 1611 edition of the KJV, the LDS Church does not currently use the Apocrypha as part of its canon.

Although story events are not triggered by the passage of time, it does determine when merchants rotate their stock.

Although a recognition of sainthood by the Pope does not directly concern a fact of divine revelation, it must still be " definitively held " by the faithful as infallible under ( at the very least ) the Universal Magisterium of the Church since it is a truth connected to revelation by historical necessity.

Although CITES is legally binding on the Parties, it does not take the place of national laws.

Although the symptoms resolve, even with treatment the infection persists and enters a chronic phase.

Although different legal processes aim to resolve many kinds of legal disputes, the legal procedures share some common features.

Although the British discovered the presence of the Argentine base in 1978, protested and tried to resolve the issue by diplomatic means, no effort was made to remove them by force until after the Falklands War.

Although the Peace of Augsburg created a temporary end to hostilities, it did not resolve the underlying religious conflict, which was made yet more complex by the spread of Calvinism throughout Germany in the years that followed.

Although the existence of WIMPs in nature is hypothetical at this point, it would resolve a number of astrophysical and cosmological problems related to dark matter.

Although not specifically intended to resolve, or address claims of a " Lost Colony " at Roanoke, Special Indian Agent Orlando M. McPherson of North Carolina in response to a Senate Resolution in 1914 completed an investigation into the Indians of North Carolina.

Although the poem states that he fled " from home in Spain / Going down to Rome with heavy spirit ," this does not resolve the question of what intermediate journeys Ibn Ezra may have made before settling in Rome, possibly in the company of R ' Yehudah HaLevi.

Although most historical linguists believe this is unlikely, it is not yet possible to resolve the issue.

However, on October 28, 2008, McKenna said that he would not be seeking the leadership, saying " Although I have been deeply moved by expressions of support for me from across the country, I have not been persuaded to change my long-standing resolve to exit public life for good ," and

Although she was not active in religious politics, in 1675 Catherine was criticised for supposedly supporting the idea of appointing a bishop to England who, it was hoped, would resolve the internal disputes of Catholics.

Although he feels pain, he still has a hardy resolve and is capable of taking much punishment.

Although he enjoyed making entertainments, Ophüls became identified as a documentarian, using a characteristically sober interview style to resolve disparate experiences into a persuasive argument.

Although the attitude of the Wittenberg theologians frustrated his attempts to bring about harmonious relations, and although the situation was further complicated by the position of Georg, Margrave of Brandenburg-Ansbach, who demanded a uniform confession and a uniform church order, Philip held that the differences between the followers of Martin Bucer in and the followers of Luther in their sacramental theories admitted honest disagreement, and that Holy Scripture could not resolve the differences definitively.

Although they did not resolve the border demarcation matters, the meetings restored diplomatic communications ; by 1970, Mao understood that the PRC could not simultaneously fight the USSR and the USA, whilst suppressing internal disorder.

Although historians of Greek science have traditionally considered these models to be merely geometrical representations, recent studies have proposed that they were also intended to be physically real or have withheld judgment, noting the limited evidence to resolve the question.

Although its official purpose is to resolve name problems and new name proposals for the federal government, the Board also plays a similar role for the general public.

Although more than a quarter of a million soldiers eventually died – for which Falkenhayn was sometimes called " the Blood-Miller of Verdun " – neither side's resolve was lessened, because, contrary to Falkenhayn's assumptions, the Entente was able to replace their dead with fresh " human material " via the Noria system, which refers to French General Phillippe Pétain's practice of allowing a unit to remain for only a few days in an area of intense combat before it was replaced.

Although Commander Sinclair managed to resolve the issue in Mollari's favor, this experience would lead to him being open to Morden's temptation, which would drive much of the later events of the series.

" Although most cases of intoxication resolve without incident, there have been isolated cases with severe consequences, especially after higher dosages or persistent use.

Although an anti-communist, Surawardy won the slot of Prime minister, and appointed to head a coalition government of Pakistan in 1956, with initial target to resolve the energy crises, economical disparity, and promised to build a massive military in an arms race with the India.

British Admiral Somerville was not enthusiastic about the action, saying that it was "... the biggest political blunder of modern times and will rouse the whole world against us ... we all feel thoroughly ashamed ..." Although it did rekindle anglophobic feelings in France, the action demonstrated Britain's resolve to continue the war alone and rallied the British Conservative Party around Churchill ( although Prime Minister Churchill was not party leader ).

Although Pete is usually supportive of Clark and keeps this secret, their friendship is tested when he occasionally gets into trouble and relies on Clark to resolve his difficulties.

Although Cable successfully manipulates Domino into assassinating Flag-Smasher, he finds his own resolve shaken when faced with his ex-lover's doubts about his agenda.

Although a referendum sanctioned by the United Nations brought the part of North Borneo called Sabah into Malaysia in 1963, its status is disputed by the heirs of the Kiram branch as well as by the Philippine government ; meanwhile attempts to resolve the issue at the International Court of Justice is blocked by unwillingness of the Malaysian government.