Instead of considering the inverses for individual inputs and outputs, one can think of the function as sending the whole set of inputs, the domain, to a set of outputs, the range.

Instead, he remained south of the Loire River, where he was still able to exert some small amount of power, maintaining an itinerant court in the Loire Valley at castles such as Chinon, being customarily known as " Dauphin " still, or derisively as " King of Bourges " ( named after the town where he generally lived ), periodically considering flight to the Iberian Peninsula, and allowing the English to advance in power.

Instead of considering AR and VR as exact opposite concepts, Milgram et al.

To see why this should be true, suppose an investor is considering buying one of the two firms U or L. Instead of purchasing the shares of the levered firm L, he could purchase the shares of firm U and borrow the same amount of money B that firm L does.

Instead of enumerating reachable states one at a time, the state space can sometimes be traversed much more efficiently by considering large numbers of states at a single step.

Instead of considering additional structure, it is also possible to take into account various notions of manifold, especially piecewise linear ( PL ) and topological manifolds.

Instead, considering that lies in two-dimensional affine space as the ' hyperbola ' defined parametrically by

Instead, he boosted integration with Russia, considering the fact that its new leader, Vladimir Putin, was continuously supporting Kuchma and refusing to recognize the allegations.

Instead of considering technology as part of a larger spectrum of human activity, technological determinism sees technology as the basis for all human activity.

Instead of considering it an indepenndent branch of the family, Halpern grouped it with the languages of Oswalt's " Western " branch, suggesting the possibility that Northeastern Pomo represents a recent migration of a Northern Pomo subgroup ( Halpern 1964 ; Golla 2011: 106-7 ).

Instead, Ashton-Tate vacillated between being extremely interested in the Macintosh market, considering it a way to break out of their dBASE-dominated PC line, and then being completely ambivalent about it.

Instead, it seeks cognitive and cultural explanations of social and organizational phenomena by considering the properties of supra-individual units of analysis that cannot be reduced to aggregations or direct consequences of individuals ’ attributes or motives.

Instead of considering only the physical model of a solid, IBMR methods usually focus more on light modeling.

Instead, considering his entire opus of works and his prevalent self-commentaries on his own career and ethical motivations, it is clear he means to show how human beings, no matter how " modern " they become in sensibility, remain capable of using violence as a tool of power.

Instead Neptune was predicted using Newton's law of universal gravitation.

Instead of just establishing it as a military prison, he provided for a civil administration, with courts of law.

Instead, it presumably refers to the practice of setting law books and citing legal precedents in blackletter type, a tradition that survived long after the switch to roman and italic text for other printed works.

Instead, murder is treated as a civil crime and is covered by the law of retaliation, whereby the relatives of the victim decide whether the offender is punished with death by the authorities or made to pay diyah as compensation.

Instead of just studying Halakha, Louis Ginzberg wrote responsa, formal responses to questions of Jewish law.

Instead, it maintained a system of taxation on the production that took place in the territories that they controlled, in exchange for protecting the growers and establishing law and order in these regions by implementing its own rules and regulations.

Instead, the law compelled the authorities to sell gold bullion on demand at a fixed price, but only in the form of bars containing approximately four hundred troy ounces of fine gold.

Instead the Emperors reserved the implementation of the bishops of their proprietary church for themselves, defying the fact that according to canon law they were part of the transnational Catholic Church.

Instead, international law has been used with respect to the specific categories of weapons within WMD, and not to WMD as a whole.

Instead of studying law, he tinkered with mechanical gadgets.

Instead of executing Mulan as the law requires, Li Shang decides to spare her life by leaving her on the mountain as the rest of the army departs for the Imperial City to report the news of the Huns ' demise.

Instead of executing Mulan as the law requires, Li Shang decides to spare her life, leaving her on the mountain as the rest of the army departs for the Imperial City to report the news of the Huns ' demise.

Instead, appeals courts review decisions of trial courts for errors of law.

Instead, law enforcement is the responsibility of the county Sheriff, who is a constitutional officer elected every four years.

Instead, opponents denounced the law as a concession to the slave power of the South.

Instead, it contended that the law separated the two races as a matter of public policy.

Instead, the overarching story of all five seasons of the series pitted Angel as the central player in a battle between the " good " Powers That Be and the " evil " law firm Wolfram & Hart and his possible role in a prophesied apocalypse.

Instead, the court held that the right to the assistance of counsel was a fundamental right, essential for a fair trial, thereby emphasizing the procedural safeguards needed for due process of law.

Instead, the Apalachin Meeting turned into a terrible fiasco when law enforcement raided the meeting.

Instead, they were proponents of natural law, created by the King's authority, not by any individual judge.

Instead, he has worked towards establishing reliable political customs when transitioning one government administration to another, emphasizing constitutional law and protocol, and representing the Spanish State domestically and internationally, all the while maintaining a professionally non-partisan yet independent monarchy.

Instead of transparently enforcing the rule of law and being subject to public scrutiny as ordinary police agencies do, secret police organizations are specifically intended to operate beyond and above the law in order to suppress political dissent through clandestine acts of terror and intimidation ( such as kidnapping, coercive interrogation, torture, internal exile, forced disappearance, and assassination ) targeted against political enemies of the ruling authority.

Instead, Stevens was offered a job with the Fairbanks, Alaska, law firm of Emil Usibelli's Alaska attorney, Charles Clasby, whose firm – Collins and Clasby – had just lost one of its attorneys.

Instead, some of the statements turn out to be equivalent to the axiom of choice ( AC ), while others — the Boolean prime ideal theorem, for instance — represent a property that is strictly weaker than AC.

Instead, these authors invoke a usual form of the local axiom of choice, and an " axiom of replacement ," asserting that if the domain of a class function is a set, its range is also a set.

Instead of giving themselves spontaneously to the orgiastic release that jazz can give them, they undergo psychoanalysis or flirt with mysticism or turn to prostitutes for satisfaction.

Instead of closing the house in first ( as most builders do ) you can now cut your costs by not closing it in until you have to ( see p 121 ).

Instead, the audience can sit back at ease and, from the perspective of an enlightened time which no longer believes in such things, enjoy the dead seriousness with which the characters in the play take the witches and devils which are under discussion.

Instead of her old confidence in the simplest, purest, most moving musical expression, Miss Schwarzkopf is letting herself be tempted by the classic sin of artistic pride -- that subtle vanity that sometimes misleads a great artist into thinking that he or she can somehow better the music by bringing to it something extra, some personal dramatic touch imposed from the outside.

Instead, they can agree that certain paradigms should be treated in certain ways, and then agree on the similarities, the so-called warrants between a paradigm and the case at hand.

Instead of listing every single element, sometimes an ellipsis ("...") is used, if the writer believes that the reader can easily guess what is missing ; for example, presumably denotes the set of integers from 1 to 100.

Instead of conductivity, a reciprocal quantity called resistivity ρ, can be used:

Instead, a very vivid feeling can form.

Instead, with the topology of compact convergence, C ( a, b ) can be given the structure of a Fréchet space: a locally convex topological vector space whose topology can be induced by a complete translation-invariant metric.

Instead the broadcast can use the channel to include PSIP and can also subdivide across several video subchannels ( aka feeds ) of varying quality and compression rates, including non-video datacasting services that allow one-way high-bandwidth streaming of data to computers like National Datacast.

Instead of enabling the guest operating system to dialog with hardware, virtual device drivers take the opposite role and emulate a piece of hardware, so that the guest operating system and its drivers running inside a virtual machine can have the illusion of accessing real hardware.

Instead, India launched EDUSAT, an education satellite that can reach more of the country at a greatly reduced cost.

Instead, education officials across the world believe that by setting clear, achievable, higher standards, aligning the curriculum, and assessing outcomes, learning can be increased for all students, and more students can succeed than the 50 percent who are defined to be above or below grade level by norm referenced standards.

Instead the differentiation process is studied using E. invadens, a reptilian parasite that causes a very simiilar disease to E. histolytica and which can be induced to encyst in vitro.

Instead of directly modifying an FFT algorithm for these cases, DCTs / DSTs can also be computed via FFTs of real data combined with O ( N ) pre / post processing.

Instead of stacking the PC and CC registers ( normal 6809 behavior ) the FIRQ interrupt can be set to stack the entire register set, as the IRQ interrupt does.

Instead of importing a factor of production, a country can import goods that make intensive use of that factor of production and thus embody it.

Instead of having to carry around hundreds of CD-Gs or laserdiscs, KJs can " rip " their entire libraries onto their hard drives and play the songs and lyrics from the computer.

Instead of a tuilik, most traditional kayakers today use a spraydeck made of waterproof synthetic material stretchy enough to fit tightly around the cockpit rim and body of the kayaker, and which can be released rapidly from the cockpit to permit easy exit.

Instead, for him, the idea of an " infectious idea " can be a useful conceit if used under certain conditions.

Instead of picking up a newspaper, or watching the 10 o ' clock news, people can log onto the internet to get the news they want, when they want it.