Without the axiom of choice, these theorems may not hold for mathematical objects of large cardinality.

Without self-replication, capital and assembly costs of molecular machines become impossibly large.

Without large sums money, a candidate has very little chance of achieving their goal.

Without an article, the term can refer to the entirety of humanity ( also: " society in general ", " society at large ", etc.

Without sufficient dissolved oxygen in the water, animals and plants may die off in large numbers.

Without large grazers, fire-cleared areas are quickly colonized by grasses, and with enough rain, tree seedlings.

Without doubt, however, the most important and celebrated part of the Prado's drawings collection is the large group of works by Goya, numbering more than 500.

Without a corresponding fall in birth rates this produces an imbalance, and the countries in this stage experience a large increase in population.

Without leveling, grain and chaff slide to one side of separator and come through the machine in a large ball rather than being separated, dumping large amounts of grain on the ground.

Without such controls, large numbers of rural residents undoubtedly would move to the overcrowded cities in search of better living standards, work, or education.

Without the capital required to buy large tracts, they entered into a partnership with pirate Jean Lafitte in 1818 to raise money.

After a further trip to Africa, abridged by the necessities of his position as a pensioner of the school of Rome, he painted Judith, then, in 1870, Salomé, and, as a work due from the Roman school, dispatched from Tangier the large canvas, Execution Without Hearing Under the Moorish Kings, in which the painter had played with the blood of the victim as if he were a jeweller toying with rubies.

( Without an accepted definition of large cardinal property, it is not subject to proof in the ordinary sense ).

Without these wells and cisterns, the central route could no longer be used by large forces.

Without colonization he said that it would be wrong for emancipated slaves to be treated as " underlings ," but that there was a large opposition to social and political equality, and that " a universal feeling, whether well or ill-founded, cannot be safely disregarded.

Without the size constraints of smaller hearing devices body worn aid designs can provide large amplification and long battery life at a lower cost.

Without a contract with the Leafs for the 1972-73 season, Parent signed a large contract with the Miami Screaming Eagles of the newly forming World Hockey Association.

Without specific requirements for service to the local community of license, stations could be constructed in large number by out-of-region broadcasters who feed transmitters via satellite and offer no local content.

Without proper control mechanisms in place, the region's opening would disproportionately benefit government-connected business groups while displacing large numbers of the non-ethnic Lao groups currently living in the area.

Without an enlarger, only a contact print would be possible, and large images would require large size negatives and hence very large cameras.

Without an official curator, the painting collection was only available to be seen by appointment with the city clerk, a situation that has remained up to the present day for the large pieces still located there, such as the whalebone from Willem Barentsz trip to Nova Zembla or the portrait of Kenau Simonsdochter Hasselaer.

Without the huge marketing budgets of mainstream publishers, their products almost never get as much recognition or popular acclaim as those of larger publishers such as Sony, Microsoft, or Nintendo.

Without these specified — and preferably quantified — activities the plan cannot be monitored, even in terms of success in meeting its objectives. It is these programs and activities which will then constitute the " marketing " of the organization over the period.

Without any formal marketing or advertising plans, news of their songs such as " That Was a Crazy Game of Poker ," " City on Down ," and " Night Shift " spread by word of mouth alone.

As of now Paramount is trying to get Without Remorse off the ground-the screenplay has to be written yet, a director has to be picked and it still needs a budget.

Without political experience or an established party machine, Sáez was happy to rely on experts, and " hired top-notch administrators and listened to their advice about everything from setting the budget to running public services.

Without enough votes to override President Clinton's veto, Newt Gingrich led the Republicans not to submit a revised budget, allowing the previously-approved appropriations to expire on schedule, and causing parts of the Federal government to shut down for lack of funds.

Without a music budget that he was used to, Lava was forced to work with a much smaller orchestra to record his scores.

" Without a clear Sinhala connection, they suggest one from the Tamil language instead: anai-kondra ( anaik-konda ), meaning " which killed an elephant .” Per National Geographic, the word anaconda comes from the Tamil word anaikolra, which means elephant killer.

Without clear documentation, software can be hard to use — especially if it is very specialized and relatively complex like Photoshop or AutoCAD.

" Without these questions there is no clear fulcrum on which to balance law, politics, and the practice of arbitration — in fact, no common assumptions of all participants — so the ability to formulate the questions are prior to rights balancing.

Without any statutory change, the managerial functions of Ministries would be hived off into Executive Agencies, with clear Framework Documents setting out their objectives, and whose chief executives would be made accountable directly ( in some cases to Parliament ) for performance.

Without any inhibitions of any kind, I make it clear that Australia looks to America, free of any pangs as to our traditional links or kinship with the United Kingdom.

Without a specification of implementation guidelines there is a very clear likelihood that systems based on the same officially standardised specifications do not understand each other due to implementation dialectal problems.

Without entering into the debate over whether such a distant airport would make any sense at all, it is quite clear that merging both regions would create strong rivalries between Toulouse and Bordeaux, which are competitors economically speaking, not to mention the almost impossible task of choosing which of the two cities should become the capital of the new region.

Without this " specific intent ", there is insufficient evidence that the accused is the clear danger as feared because, at any time before the commission of the full offense, the accused may change his or her mind and not continue.

Without Golding's translation, common knowledge of the ancient text would not have been understood in the same clear light.

Without extending the height, the wrenches to remove caps would not clear and the break flanges for traffic models would not be located correctly in case they were hit.

Without a clear plan for his future he asked his mother if he could live abroad for a while.

Without that evidence Curtin was found not guilty, the judge declaring that the case was " crystal clear ".

:“ Without permission of the copyright holder, and in clear violation of applicable law, Defendants have copied and sold these Vaad Works and kept the proceeds for themselves … In violation of Federal and State Laws, Defendants have pocketed millions of dollars in revenues that rightfully belonged to Plaintiffs, who would have used the money to continue publishing and disseminating the teachings of the Rebbe .”( page 3 )

Without a clear opportunity to amend the application, hopes for an FM radio station were put in limbo.

Without a clear programme of government reforms to promote, he tended to moralise or equivocate.

Without timeboxing, projects usually work to a fixed scope, such that when it is clear that some deliverables cannot be completed, either the deadline slips ( to allow more time ) or more people are involved ( to do more in the same time ).

Without any clear discussion, Munro-Hay identifies him with a king Alla Amidas, who is also known only through the coins he issued.

Without any clear enemy to fight, brutality against civilians became more common.