However, that particular case is a theorem of Zermelo – Fraenkel set theory without the axiom of choice ( ZF ); it is easily proved by mathematical induction.

However, according to Josephus, in Antiquities, Book 7, Chapter 1, Joab had forgiven Abner for the death of his brother, Asahel, the reason being that Abner had slain Asahel honorably in combat after he had first warned Asahel and had no other choice but to kill him out of self defense.

However, one can choose the index of the first element by an appropriate choice of the base address B.

However, if none of the larger parties can receive enough votes to form their preferred coalition, a grand coalition might be their only choice for forming a government.

However, the choice of a husband might also provoke political instability or even insurrection.

However the situation is different when the language is of arbitrary large cardinality since then, though the completeness and compactness theorems remain provably equivalent to each other in ZF, they are also provably equivalent to a weak form of the axiom of choice known as the ultrafilter lemma.

However, with the proper choice of h, one can use the technique of rolling hash to compute all those hashes with an effort proportional to k + n.

However, environmental and safety issues exist with the choice of vegans.

However, economic dilution must prevail towards accounting dilution when making the choice.

However, like methadone, buprenorphine produces similar cognitive dehabilitation in multiple areas of mental function in both memory and timed choice task tests, which may persist after cessation of substitution treatment.

However, in certain axiom systems for constructive set theory, the axiom of choice does imply the law of the excluded middle ( in the presence of other axioms ), as shown by the Diaconescu-Goodman-Myhill theorem.

However, some species exhibit sex-role reversed behavior in which it is males that are most selective in mate choice ; the best-known examples of this pattern occur in some fishes of the family Syngnathidae, though likely examples have also been found in amphibian and bird species.

However, combining delegation with first-past-the-post may be a better choice because that way Charlie can give his votes to Fran instead of seeing them handed to Bob following the runoff.

However the Holy Roman Emperor Otto I ( 936 – 973 ) did not approve of the choice and had him deposed after only a month with his acquiescence.

However, Principia Mathematica required, in addition to the basic axioms of type theory, three further axioms that seemed to not be true as mere matters of logic, namely the axiom of infinity, the axiom of choice, and the axiom of reducibility.

However, a 2007 meta-analysis concluded that " pair programming is not uniformly beneficial or effective " because many other factors besides the choice of whether to use pair programming have large effects on the outcome of a programming task.

However, the legislation of Pope Nicholas II ( in the famous decree of 1059 ) pre-empted the choice of the majority of the cardinal priests and cardinal deacons.

However, whereas in Quake, the only option was to change the color of the player's uniform unless third party modifications were used, now the game comes with a selection of three different player models: a male marine, a female marine, and a male cyborg ; choice of player model also affects the speech effects the player's character will make, such as exhaling in effort while jumping or groaning when injured.

However, for the rejected pilot " The Cage " ( 1964 ), Roddenberry went with director Robert Butler's choice of John Hoyt to play Dr. Philip Boyce.

However, the unified nature of spacetime and the freedom of coordinate choice it allows imply that to express the temporal coordinate in one coordinate system requires both temporal and spatial coordinates in another coordinate system.

However, if the relation in question is already well-ordered, one can often use transfinite induction without invoking the axiom of choice.

However, the Court struck down the " choice of expenditure " rule, which required that parties could either make coordinated expenditures for all its candidates, or permit candidates to spend independently, but not both, which they agreed " placed an unconstitutional burden on the parties ' right to make unlimited independent expenditures.

However, these may all be different if the axiom of choice fails.

However, the decomposition of a vector into components is not unique, because it depends on the choice of the axes on which the vector is projected.

However, the choice to become vegetarian for non-medical reasons can sometimes be controversial.

However, Mark Antony, with a subtle and eloquent speech over Caesar's corpse — beginning with the much-quoted " Friends, Romans, countrymen, lend me your ears "— deftly turns public opinion against the assassins by manipulating the emotions of the common people, in contrast to the rational tone of Brutus's speech.

However, in the middle of the Battle of Actium, Cleopatra flees with her sixty ships, and Antony follows her, leaving his army to ruin.

As Janet Adelman observes, “ almost all the central elements in Antony and Cleopatra are to be found in the Aeneid: the opposing values of Rome and a foreign passion ; the political necessity of a passionless Roman marriage ; the concept of an afterlife in which the passionate lovers meet .” However, as Heather James argues, Shakespeare ’ s allusions to Virgil ’ s Dido and Aeneas are far from slavish imitations.

However, Harris points out that Caesar and Antony both possess an uncontrollable desire for Egypt and Cleopatra: Caesar ’ s is political while Antony ’ s is personal.

However, on the other side of the via Egnatia, Antony was able to storm Cassius ’ fortifications, demolishing the palisade and filling up the ditch.

However, Mark Antony and Cleopatra were defeated by Octavian at the Battle of Actium in 31 BC.

However, images from the war, especially the concentration camps, continued to haunt her and she started on what Antony describes as a " downward spiral ".

However, his Master of the Horse Marc Antony fired up his troops and after several attempts broke Libo's blockade and managed to make it north of Caesar's position.

However, unaware of the war, Antony was still in the eastern provinces, and his legions were unsure of his commands and did not assist Lucius.

However, most historians place the end of the Republic a decade later, after the final showdown between Augustus and Mark Antony at the Battle of Actium, in 31 BC.

However, after Antony Cotton auditioned for the production team, Davies and his fellow producers felt they had no choice but to offer the role to him instead of Collinson.

However, the society has always been a focal point for an international think-tank movement ; Hayek himself used it as a forum to encourage members such as Antony Fisher to pursue the think-tank route.

However, Travis resurrected the label in the late 90s, finding success with The Libertines, The Strokes and Antony and the Johnsons.

However, in the 2004 Federal Election, an energetic campaign by Dr Andrew Laming, and an electoral redistribution ( due to the creation of the new Division of Bonner ), saw Bowman returned to the Liberal Party by a significant margin ( 59. 12 % two party preferred ) and the division was then considered by pollsters such as Antony Green to be a fairly safe Liberal seat.

However he resigned in March 1994 after it was revealed by Max Clifford and the News of the World that he had an affair with Lady ( Bienvenida ) Buck, the wife of Conservative MP Antony Buck.

However, Price and Coleman married in 2007 ; and while they divorced in 2008, Price claimed in a court petition that she remained Coleman's common-law wife, sharing bank accounts and presenting themselves publicly as husband and wife, until his death ; an assertion that, if validated by the court, would make her the lawful heir.

However, in May 2012 Judge James Taylor ruled that while Price had lived in Coleman's home after their marriage ended, their relationship at the time of his death failed to meet Utah ’ s standard for a common-law marriage.

However, the overdriven sound of the Hammond gained a new image when it became part of 1960s and 1970s rock with artists like Alan Price, Gregg Allman, Steve Winwood, Rick Wright, Keith Emerson, Jon Lord, Matthew Fisher, Rick Wakeman, Tony Banks and Jack McDuff.

" However, in 1968, Buechner received a letter from Charles Price, the chaplain at Harvard, inviting him to give the Noble Lectures series in the winter of 1969.

However, Lost Springs mayor Leda Price claims the census was inaccurate, and that Lost Springs had four residents in 2000.

However Kaye-Smith generously allows Lucia to succeed: her novel The Price of Bread is published ( by a left-wing book club ) and becomes a success.

However, Sobeys has announced that it plans to convert most of the remaining IGA stores in Ontario to the Price Chopper, Foodland, or Sobeys banners.

However his suggestion was bluntly rejected by Wood, Bevan and Price, the other three members, so Wayne finally quit the group in January 1970.

However, he was involved in a relationship with Price model Dian Parkinson from 1989 to 1991, which ended in legal action.

However in 1734 Bishop Arthur Price ( 1678-1752 ) decided to replace the decaying mansion with a new Georgian residence.

However Price and Boswell were suitably impressed to change the Elizabeth character so that she breaks out at an older age due to a latent puberty.

However, he was defeated in a bid for re-election in 1986 by the Democrat David Price.

However, all recorded forms show this N. That is the reason why Liam Price says it is probably a Norwegian place-name and A. Sommerfelt gives it as a former Vikinga-ló and understands it as " the Vikings ' meadow ".

However, from 26 March 2008, speed auction " flipped the arrow " and started selling all its products using a falling price dynamic, matching its sister channels Bid and Price Drop.

However, there has never been a case where the Act has been successfully invoked to allow travellers to remain on greenbelt land, and indeed the prospects of this ever happening seem highly unlikely after the House of Lords decision in Kay and others and another v. London Borough of Lambeth and others heard with Price v Leeds City Council which severely restricted the occasions on which Article 8 may be invoked to protect someone from eviction in the absence of some legal right over the land.

However, the Union forces were in a dominating position, and Lyon chased Jackson and Price to the far southwest of the state.

However, at the beginning of 2008, the Market Price History was also made free of charge for all users, still giving up to a 12 month view of historical sales data for any release.

However, the Korean War brought a return to the same inflationary pressures, and price controls were again established, this time under the OPS ( Office of Price Stabilization ).

However, in September 1972, CBS launched The New Price is Right at 10: 30 / 9: 30 and drained off more than half of the Concentration audience.

However, Martindale already chose to host Gambit, another of the three game shows that premiered on the same day in 1972 on CBS ( New Price also debuted that day ).

However the same Price / Demand relationship yields $ 4000 if consumers are presented with multiple prices.

However, this changes when Orrin Price ( Morton Downey, Jr .), becomes a member of the Adams College Board of Regents and a new generation of jocks come to campus, including Orrin's obnoxious son and a brain-dead jock named Bobo.

However, both daughters he had with Clarice Price, Gwynne and Emma, object to one particular film being displayed, as it depicts them naked as young children.