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 " Amazing Grace " set to " New Britain " was popular, other versions existed regionally.

Although there are no set minimum admissions criteria for Barrett College, the average GPA of incoming freshmen was 3. 84, with average SAT scores of 1314 / 1600 and ACT scores of 29.

Although Rodin is generally considered the progenitor of modern sculpture, he did not set out to rebel against the past.

Although he had for many years " harbored an ambition to create work for a public square ", he " had never set foot in New York, and knew nothing about life in a rapidly evolving metropolis.

Although the Umayyads did not have a historical presence in the region ( no member of the Umayyad family was known to have ever set foot in al-Andalus before ) and there were grave concerns about young Abd al-Rahman's inexperience, several of the lower-ranking Yemenite commanders felt they had little to lose and much to gain, and agreed to support the prince.

Although Zermelo's fix allows a class to describe arbitrary ( possibly " large ") entities, these predicates of the meta-language may have no formal existence ( i. e., as a set ) within the theory.

Although Benedictines do not take a vow of silence, hours of strict silence are set, and at other time silence is maintained as much as is practically possible.

Although each series is set in a different era, all follow the " misfortunes " of Edmund Blackadder ( played by Atkinson ), who in each is a member of a British family dynasty present at many significant periods and places in British history.

Although passengers rarely have cause to refer to either document, all travel is subject to the National Rail Conditions of Carriage and all tickets are valid subject to the rules set out in a number of so-called technical manuals, which are centrally produced for the network.

Although counting the number of elements in a set is a rather broad mathematical problem, many of the problems that arise in applications have a relatively simple combinatorial description.

Although the individual philosophical schools differ considerably, they nevertheless share a common vocabulary and set of concerns.

Although a " bijection " seems a more advanced concept than a number, the usual development of mathematics in terms of set theory defines functions before numbers, as they are based on much simpler sets.

Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle thirds of a line segment.

Although Cesare Borgia's father gave him the power to set up, Cesare ruled the Romagna with skill and tact for the most part.

Although Celera was originally set to sequence a composite of DNA samples, partway through the sequencing, Venter switched the samples for his own DNA.

Although these guidelines have been widely implemented, opponents argue that even when a diagnostic criteria set is accepted across different cultures, it does not necessarily indicate that the underlying constructs have any validity within those cultures ; even reliable application can only demonstrate consistency, not legitimacy.

Although rumors of drug use and other " problems on the set " swirled around her dismissal, the producers were adamant that the pregnancy was the only reason her character was written out.

Although various notations are used throughout the literature to denote that two elements a and b of a set are equivalent with respect to an equivalence relation R, the most common are " a ~ b " and " a ≡ b ", which are used when R is the obvious relation being referenced, and variations of " a ~< sub > R </ sub > b ", " a ≡< sub > R </ sub > b ", or " aRb ".

Although he doled out offices, money, and titles mainly to Christian highlanders in the hope of co-opting would-be Eritrean opponents in early 1967, the imperial secret police of Ethiopia also set up a wide network of informants in Eritrea and conducted disappearances, intimidations and assassinations among the same populace driving several prominent political figures into exile.

Although definitions of ecosystem management abound, there is a common set of principles which underlie these definitions.

Although unsure as to why these saints should choose such a " sinner " as their patron, Einhard nonetheless set about ensuring they continued to receive a resting place fitting of their honour.

Although formal certification of his freedom from Burghley's control was deferred until May 1572, Oxford was finally granted the income of £ 666 which his father had intended him to have earlier, but properties set aside to pay his father's debts would not come his way for another decade.

Although individual buses are generally owned by individuals or small companies, the timetables, fares, and levels of service are set by Strandfaraskip Landsins and the government.

Although the area was originally settled in 1733, Moncton is considered to have been officially founded in 1766 with the arrival of Pennsylvania Dutch immigrants from Philadelphia.

Although the Packers lost 17 – 13 to the Philadelphia Eagles, they had sent a clear message that they were no longer losers.

Although the Tigers have been the predominant MLB parent of the IL Mud Hens ( 1967 – 73 and since 1987 ), the team has also been affiliated with the Philadelphia Phillies ( 1974 – 75 ), Cleveland Indians ( 1976 – 77 ), Minnesota Twins ( 1978 – 86 ) and the Yankees ( 1965 – 66 ).

Although there were less in this decade than there were in the 1990s, the 2000s still saw many popular and notable sitcoms, including Will and Grace, Malcolm in the Middle, The King of Queens, Arrested Development, How I Met Your Mother, Scrubs, Curb Your Enthusiasm, The Office, Two and a Half Men, The Big Bang Theory, It's Always Sunny in Philadelphia, and 30 Rock, among many others.

Although they lost their first-round series in six games to the Philadelphia Flyers, it still remains a magical season for Lightning fans.

Although Arnold had already been secretly negotiating with the British over a change of allegiance since May 1779, this news contributed to his decision to resign the command of Philadelphia.

Although deactivated shortly after they were added, ramp meters have been reactivated at select interchanges of Interstate 476 in suburban Philadelphia.

Although the Welsh Tract was originally meant to be a self-ruling municipality, it was divided between Chester County and Philadelphia when that county was created in 1685, and the Welsh subsequently submitted to the authority of Chester County.

" Although later, at Wizard World Philadelphia 2009 she said she didn't realize it was going to be abrupt and without fanfare, and would have appreciated a little something more.

Although the Can-Am League never operated with more than six teams, after the 1935 – 36 season it reduced down to just four member clubs – Springfield, Philadelphia, Providence, and New Haven – for the first time in its history.

Although Howe would have preferred to make a landing on the Delaware River below Philadelphia, reports of well-prepared defences dissuaded him, and the fleet spent almost an entire extra month at sea to reach Head of Elk.

Although Dallas is located in the south-central United States, the Cowboys are a member of the NFC East division due to their long-standing rivalries with the New York Giants, Philadelphia Eagles, and Washington Redskins, all of whom are located on the Eastern seaboard.

Although having moved into its permanent venue at PPL Park, the Philadelphia Union continue to use the Linc for matches where ticket demand is expected to far exceed the full capacity at its regular home.

Although Sunday played well in his thirty-one games with Philadelphia, the team finished in third place.

Although he typically demonstrated little emotion on the field ( and was known as " Captain Cool " by many in Philadelphia sports circles ), Schmidt surprised many with an emotional, and occasionally tearful, retirement speech.

Although the Stars had a strong following, Tanenbaum knew he couldn't hope to compete with the Philadelphia Eagles and moved the team to Baltimore.

Although he played in a career-high 82 games in his first season in with the 76ers, it was also in Philadelphia that Bol's production as a player began to decline ( in terms of both games played and per game statistics ).

Although she did not see her Bird Girl sculpture achieve fame, she was already a renowned sculptor whose pieces have been on display in such locations as the Philadelphia Museum of Art, the Whitney Museum of American Art in New York, the White House, and the Massachusetts State House.

Although the film was exposed as a hoax in Variety in 1976, it became popular in New York, Philadelphia, Los Angeles and Boston.

Although fire engines from nearby cities ( such as Philadelphia and Washington, D. C. as well as units from New York City, Virginia, Wilmington, and Atlantic City ) responded, many could not help because their hose couplings could not fit Baltimore's hydrants.

Although this ended his 1909 season, he recovered by 1910 to become a star pitcher again, finishing with a 29-11 record for the Syracuse Stars in the Class B New York State League, before being sold to the Philadelphia Phillies for $ 750.

Although Carrera ’ s movement never benefited from the experience of these French officers, Poinsett did succeed in obtaining contracts with the firm D ’ Arcy and Didier of Philadelphia to supply arms for the expedition which Carrera was planning.

Although philosophe is a French word, the Enlightenment was distinctly cosmopolitan ; philosophes could be found from Philadelphia to St. Petersburg.

Although the first American pasta " factory " opened in Philadelphia in 1798, most pasta factories emerged with the rapid American industrialization following the American Civil War.