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

Without these APIs, the programmer needs to write these APIs him / herself.

Without much added cost, these devices could be designed to also harvest BSFL.

" 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 such logical operators of valence 0, these two constants can only be expressed using quantifiers.

Without these precautions, cracks in overgrown and overly brittle hoof walls are a danger, as is bruising of the soft tissues within the foot because of inadequately thick and hard sole material.

Without some earlier ones, such as the spinning jenny and flying shuttle in the textile industry and the smelting of pig iron with coke, these achievements might have been impossible.

Without these crutches, reading a Kvikkalkul program requires one to work out what the program actually does.

Without glacial sources, annual flow regimes in these rivers are more variable although limited flow persists through the dry season.

Without these two events, Italian unification would have been a more prolonged process.

Without these features, they are usually noncompliant.

Without at least one of these two pieces of information, we are not obviously justified in seeing design in such cases … he problem for the fine-tuning argument is that we lack both of the pieces that are needed to justify an inference of design.

Without water, these particular metabolic processes could not exist.

Without appropriate intervention, these children lag behind their peers.

Without the transfer of these rights, Tufts could come in at any time and demand the removal of buildings to obtain minerals.

Without the bright flame and dense smoke trail produced by the burning of aluminized propellants, these smokeless propellants all but eliminate the risk of giving away the positions from which the missiles are fired.

Without good flexing properties these movements rapidly form cracks and, ultimately, make the rubber article fail.

Without these opaque layers, the hot, luminous core emits ultraviolet radiation that ionizes the ejected outer layers of the star.

Without halftoning, the three primary process colors could be printed only as solid blocks of color, and therefore could produce only seven colors: the three primaries themselves, plus three secondary colors produced by layering two of the primaries: cyan and yellow produce green, cyan and magenta produce a purplish blue, yellow and magenta produce red ( these subtractive secondary colors correspond roughly to the additive primary colors ) plus layering all three of them resulting in black.

Without social capital in the area of education, teachers and parents that play a responsibility in a students learning, the significant impacts on their child ’ s academic learning can rely on these factors.

Without sufficient levels of these key electrolytes, muscle weakness or severe muscle contractions may occur.

Without trying to make a direct analogy one can be convinced of the importance of considering these extra properties following the rationale implied by this game: an object is defined here consisting of two rods and strings connecting them.

Without timely treatment, these new blood vessels can bleed, cloud vision, and destroy the retina.

Without observational constraints, there are a number of candidates, such as a stable supersymmetric particle, a weakly interacting massive particle, an axion, and a massive compact halo object.

Without massive Soviet subsidies and its primary trading partner Cuba was comparatively isolated in the 1990s, but has since entered bilateral co-operation with several South American countries, most notably Venezuela and Bolivia.

Without massive Soviet subsidies and its primary trading partner Cuba was comparatively isolated in the 1990s, but has since entered bilateral co-operation with several South American countries, most notably Venezuela and Bolivia.

Many academics have vigorously criticized UN-Habitat and the World Bank arguing that their ' Cities Without Slums ' Campaign has led directly to a massive increase in forced evictions.

Without nearby bare soil, a hardscape requires artificial methods of drainage or surface runoff in order to carry off the sometimes massive volumes of water that would normally be mostly absorbed into the ground as groundwater.

Without deregulation in the railway industry permitting abandonment or sale of a railway line, or even the ability to set prices to match those of trucks, both CNR and CPR paid dearly for owning these inefficient lines.

Without highways of access, the route had to be done on horse, in long and painful caravans from the coast, or by the rivers from the region of the east.

Without money or property, what would you have had at Baton Rouge ''??

Without the decay of a sense of objective reference ( except as the imitation of mystery ), the stress on subjective invention would never have been stimulated into being.

Without further inquiry, Pike jumped to the conclusion that Robinson was guilty, and, following the honorable route that would eventually lead to the dueling ground, sent a message to Robinson through his friends, demanding that he either confirm or deny his complicity.

Without the good magazines, without their book reviews, their hospitality to European writers, without above all their awareness of literary standards, we might very well have had a generation of Krim's heroes -- Wolfes, Farrells, Dreisers, and I might add, Sandburgs and Frosts and MacLeishes in verse -- and then where would we be??

Without public scrutiny the deliberations of public agencies would no doubt be conducted more speedily.

Without math the men who are continually seeking the causes of and the reasons for the many things that make the world go 'round would not have any means of analyzing, standardizing, and communicating the things they discover and learn.

Without it she would have been drab and limp.

Without RIMAs or the MAOI of MAO-A, DMT would be oxidised ( and thus rendered biologically inactive ) by monoamine oxidase enzymes in the digestive tract.

Without the contrast of light, the figures would blend in with its surrounding environment.

Without a register like an accumulator, it would be necessary to write the result of each calculation ( addition, multiplication, shift, etc.

Without using the term, 1920 saw the first rule that would be referred to today as defensive indifference, as stolen bases would not be credited, unless an effort was made to stop the runner by the defense.

Without this double feedback, the system would still be bistable, but would not be able to tolerate such a wide range of concentrations.

Without a significant amount of memory, a computer would merely be able to perform fixed operations and immediately output the result.

Without adequate roads, the traffic would get rather jammed during the summer months.

Without Salic Law, upon the death of John I, the crown would have passed to his half-sister, Joan ( later Joan II of Navarre ).

Without them, they would be unable to obtain any nutritional value from plants.

If only layer C changes, we should find a way to avoid re-blending all of the layers when computing F. Without any special considerations, four full-image blends would need to occur.

Without an Afghan say in the matter, the Joint Anglo-Russian Boundary Commission agreed the Russians would relinquish the farthest territory captured in their advance but retain Panjdeh.

Without it, household behavior would be unaffected by uncertain employment and income prospects, financial and capital markets would reduce to exchange of a single instrument in each market period, and there would be no communications industry.

Without money to facilitate easy comparisons, non-market socialism lacks any way to compare different goods and services and would have to rely on calculation in kind.