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 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, Israel has been unfaithful to God by following other gods and breaking the commandments which are the terms of the covenant, hence Israel is symbolized by a harlot who violates the obligations of marriage to her husband.

" However, some Complementarian authors caution that a wife's submission should never cause her to " follow her husband into sin.

However, Paul indicates that bishops, deacons, and elders must have one wife, and that women must have one husband:

However, modern historians allege that the baptism of Mieszko I was dictated by political benefits and should not be attributed to any action of Dobrawa, who according to them had virtually no role in the conversion of her husband.

However, until a husband was found, the King had the legal right to Eleanor's lands.

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, as was prevailing tradition, the adolescent bride was to spend much time at her parents ' house, and away from her husband.

However, she was an alcoholic and often had to be brought home from Chicago bars by her husband ; she finally joined Alcoholics Anonymous.

However, two others have called, making Ender's trip not entirely in vain: they are Novinha's eldest son Miro, calling for someone to speak the death of Libo, who was killed the same way his father was ; and Novinha's eldest daughter Ela, calling for someone to speak the death of Novinha's husband Marcos Ribeira, who died not six weeks ago from a terminal disease.

However, Boccaccio's version is unique in that the husband in the tale preserves both his honor and that of his wife, and emphasis on " keeping up appearances " that is distinct of the Renaissance merchant class, to which Boccaccio belonged.

However, everyone " Tom " passes sees a person of their own — a lost husband, a son, a criminal.

However, Becky, in a moment of conscience, shows Amelia the note that George ( Amelia's dead husband ) had given her, asking her to run away with him.

However, before the war both she and her husband, like most of Parliament and the British public, had supported appeasement and Prime Minister Neville Chamberlain, believing after the experience of the First World War that war had to be avoided at all costs.

However since the release of Antonia Fraser The Wives of Henry VIII in 1994, and David Starkey's 2004 book on the six wives, Catherine's first husband has been identified as Sir Edward Borough.

However, her mother supported her and was beaten when her husband discovered Carmen had auditioned for a radio show.

) However, Joan and Eunice decide that this possible explanation is irrelevant, and near the end of the book, a third personality, that of Joan's new husband, joins them by means that can only be explained via delusion, religion or mysticism, not science.

However, Placidia was now free, and re-joined her husband at Constantinople, where, a year later, gave him a daughter, Anicia Juliana.

However, she refused to accept this and with the help of vocal and dance lessons ( most notably with Sam Harris, Angela Bacari ), which she still takes daily, managed to recover and returned to the stage in 2001 when asked by long-time friend Michael Jackson to perform at Madison Square Garden in New York City where she sang " Never Never Land " and the televised " You Are Not Alone " at the Michael Jackson: 30th Anniversary Special concert produced by soon to be husband David Gest.

However, Martha ’ s husband Ras ( Spencer Williams ) is absent from the service – he claims he was hunting, but he actually poached a neighbor ’ s boar.

However, some time not long after the death of her husband ( Thutmose II ), Hatshepsut assumed the royal regalia and the title of pharaoh, reigning for 21 years.

However, Skaði must choose this husband by looking solely at their feet.

However, Laura in her narration stresses that what holds her back is her horror at the thought of betraying her husband and her settled moral values, tempted though she is by the force of a love affair.

However, her first marriage was characterized by a " lack of lust ", and when she met Sean Ward, a painter and yet another gentile, she left her husband for him.

However, a musical score influenced by classical Japanese music by Deren's third husband, Teiji Ito, was added under Deren's supervision in 1959.