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, in practice they proved to be too large to manoeuvre well in the close waters of estuaries and rivers, the only places in which a ' naval ' battle could occur.

However, shortly after this positive result, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems ( 1931 ), showing that in any sufficiently strong axiomatic system there are true statements which cannot be proved in the system.

However, this design proved to be very difficult to remove from the console and was replaced by a second design.

However, chlorpromazine proved to reduce the effects of psychosis in a more effective and specific manner than lobotomy, even though it was known to be capable of causing severe sedation.

" However, his looks proved to be an asset in his personal and political relationships, as his law partner William Herndon wrote, " He was not a pretty man by any means, nor was he an ugly one ; he was a homely man, careless of his looks, plain-looking and plain-acting.

However, it was ultimately unable to achieve a significant market share and proved commercially unviable for Be Inc.

However, subscription-funded digital terrestrial television ( DTT ) proved less of a competitive threat.

However the rope available at the time proved too susceptible to wear and the system was abandoned in favour of steam locomotives after eight years.

However, the PDP-6 proved to be a " hard sell " with customers, as it offered few advantages over similar machines from the better established vendors like IBM or Honeywell, in spite of its low cost around $ 300, 000.

However, the plantations, both under their previous private ownership and under government administration, proved consistently unprofitable due to the introduction of new oils and lubricants in the international marketplace, and the establishment of vast coconut plantations in the East Indies and the Philippines.

However, Thomas Crow argues that this path " proved to be less a way forward than a cul-de-sac for history painting.

However, when Baden was transferred west to fight the French in 1692 his successors, first Caprara, then from 1696, Frederick Augustus, the Elector of Saxony, proved incapable of delivering the final blow.

However, the facilities proved to be able to barely handle the flood of immigrants that arrived in the years just before World War I.

However, General Niazi proved to be a failure and ineffective ruler.

" However the Times also reflected widespread skepticism as to whether the forward pass could be effectively integrated into the game: " There has been no team that has proved that the forward pass is anything but a doubtful, dangerous play to be used only in the last extremity.

However, according to the late Tomoyuki Tanaka, it proved to be difficult to obtain permission to use King Kong.

However the Eastern Question and the resulting Crimean War proved to be the downfall of his government.

However, the rise of quiz shows proved to be short-lived.

However, a campaign to reconquer Peru and Chile during the Chincha Islands War ( 1864 – 1866 ) proved disastrous and Spain suffered defeat before the determined South American powers.

However, Paul Henreid proved to be the best player.

However, his discoveries were not appreciated by his contemporaries and came into general use only with discoveries of British surgeon Joseph Lister, who in 1865 proved the principles of antisepsis in the treatment of wounds ; However, medical conservatism on new breakthroughs in pre-existing science prevented them from being generally well received during the 19th century.

However, the lamps proved a false dawn because they became unsafe very quickly and provided a weak light.

However, his captaincy proved to be an unhappy one ; he lost form and the team did not do well.

However the data on Cobb's caught stealing is missing from 12 seasons, strongly suggesting he was unsuccessful many more times than his stats indicate.

However, Burn was unsuccessful in depriving Smith of the appointment.

However, despite claims of government corruption, favoritism of Zaghawas, and abuses by the security forces, opposition party and labor union calls for general strikes and more active demonstrations against the government have been unsuccessful.

However, the toad was generally unsuccessful in reducing the targeted beetles, in part because the cane fields provided insufficient shelter for the predators during the day.

However, these early events received little attention, and it was not until 1957, when the New York Times reported an unsuccessful struggle to restrict DDT use in Nassau County, New York, that the issue came to the attention of the popular naturalist-author, Rachel Carson.

However, attempts to establish military alliances were unsuccessful.

However, a referendum on devolution in 1979 was unsuccessful as it did not achieve the support of 40 % of the electorate ( despite a small majority of those who voted supporting the proposal.

However, a referendum on devolution in 1979 was unsuccessful as it did not achieve the necessary support of 40 per cent of the electorate ( despite a small majority of those who voted supporting the proposal ) and the SNP went into electoral decline during the 1980s.

However, his reign was far from perfect for everyone: he made unsuccessful crusades, his expanding administrations raised opposition, and he burned Jewish books at the Pope's urging.

However, as habeas corpus is only a procedural device to examine the lawfulness of a prisoner's detention, so long as the detention is in accordance with an Act of Parliament, the petition for habeas corpus is unsuccessful.

However, attempts to find appropriate short fiction companion pieces to adapt were unsuccessful and Hello Out There was never commercially released.

However, the scandals of Reagan's Secretary of Housing and Urban Development Samuel Pierce and the neglect of the president were obstacles from the start, and Kemp was unsuccessful at either of his major initiatives: enacting enterprise zones and promoting public housing tenant ownership.

However the campaign was unsuccessful, and the change may go ahead.

However, they were unsuccessful in their attempt to secure a trademark for ' open source ' to control the use of the term.

However, the Tsardom was weakened by the long and unsuccessful Livonian War against the coalition of Poland, Lithuania, and Sweden for access to the Baltic coast and sea trade.

However, Robinson's tenure lasted less than four years and was generally unsuccessful.

However, his own creative projects – such as the film Splitting Heirs ( 1993 ), a comedy he wrote, starred in and executive-produced – were mostly unsuccessful with critics and audiences.

However, this proved unsuccessful.

However database and directory administrators can take countermeasures against online attacks, for example by limiting the number of attempts that a password can be tried, by introducing time delays between successive attempts, increasing the answer's complexity ( e. g. requiring a CAPTCHA answer or verification code sent via cellphone ), and / or locking accounts out after unsuccessful logon attempts.

" However, Sun Quan was himself equally unsuccessful in efforts to make major attacks on Wei.

However, efforts to privatise the two state-owned bauxite mining companies, Berbice Mining Company and Linden Mining Company have so far been unsuccessful.

However, the expedition is unsuccessful and, on his return, he is fined in a prosecution led by Xanthippus and put in prison where he dies of wounds received at Paros.

However, he is unsuccessful in achieving these reforms, and earns the disfavour of King Agesilaus II of Sparta.

However, his attempts to abolish the appointive upper house of the NSW Parliament, the Legislative Council, were unsuccessful.

However, the attempt was unsuccessful.