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, a narrow strip may be very practical for small developments, or to provide additional stream frontage for a fisherman's trail, or include scenic strips within the park unit.

However, whether you arrange to have a European or American model, if you rent a car with the proper seating capacity in relation to the number of people in your party, your transportation expense will average very close to $10.00 per day per passenger.

However, one does not need to know very much.

However, while Apollo has a great number of appellations in Greek myth, only a few occur in Latin literature, chief among them Phoebus ( ; Φοίβος, Phoibos, literally " radiant "), which was very commonly used by both the Greeks and Romans in Apollo's role as the god of light.

However, only a very small percentage of all these people has remained in Angola, either for personal reasons ( intermarriage ) or as professionals ( e. g. medical doctors ).

However, very small amounts of steel, ( an alloy of iron and around 1 % carbon ), was always a byproduct of the bloomery process.

However, applets have very little control over web page content outside the applet dedicated area, so they are less useful for improving the site appearance in general ( while applets like news tickers or WYSIWYG editors are also known ).

However, it would have been very slow.

However I will come to Sardis, as I think it very desirable to become a friend of yours.

However, virtually all major works of Greek and Latin prose possessed such clausulae ; and some scholars have rejected the identification of Libanius ' Marcellinus with Ammianus, since Marcellinus was a very common name and the tone suggests Libanius was addressing a man much younger than himself ( Ammianus was his contemporary ).

However, since Paul was from Cilicia and refers to himself using this name ( see Acts 21: 39, 22: 3 ), it seems very natural that the name Cilicia would have continued to be in colloquial use among its residents despite its hiatus in official Roman nomenclature.

However, even with Mozart and Salieri being rivals for certain jobs, there is very little evidence that the relationship between the two composers was at all acrimonious beyond this, especially after 1785 or so when Mozart had become established in Vienna.

However these mechanical systems were slow, the images were dim and flickered severely, and the image resolution very low.

However, very broadly, artillery units are assigned in direct support or in general support.

However, very few prototypes have been located, due to Tramiel Atari ’ s reluctance to make them in the first place.

However, it is more correct for a very slender plate when the angle becomes large and flow separation occurs, or if the flow speed is supersonic.

However, the first major pop rapper from Belgium was Benny B, who had a very mainstream and commercial sound.

However travel through very remote areas, on isolated tracks, requires planning and a suitable, reliable vehicle ( usually a four-wheel drive ).

However, they remain very stiff even after thorough cooking, and if swallowed whole or in large pieces, they may pose a risk of scratching the digestive tract or even causing choking.

However, Marlborough was convinced of the urgency – " I am very sensible that I take a great deal upon me ", he had earlier written to Godolphin, " but should I act otherwise, the Empire would be undone ..."

However, the concentration of gold in its ore is in general very low.

However, the purchase of a Scottish estate by Victoria and Albert, and their adoption of Scottish architectural style, was very influential for the ongoing revival of Highland culture.

However, the tree constructed by the living tree project, a collaboration between ARB-Silva and LPSN where a 16S ( and 23S if available ) tree of all validated species was constructed, the genus Bacillus contains a very large number of nested taxa and majorly in both 16S and 23S it is paraphyletic to Lactobacillales ( Lactobacillus, Streptococcus, Staphylococcus, Listeria, etc.

However practice was variable: very high attendance at festivals was in most places the order of the day and in some places regular communion was very popular, in other places they stayed away or sent " a servant to be the liturgical representative of their household.