Given a field F, the assertion “ F is algebraically closed ” is equivalent to other assertions:

Given that both A and not-A are seen to be “ true ,” Kant concludes that it ’ s not that “ God doesn ’ t exist ” but that there is something wrong with how we are asking questions about God and how we have been using our rational faculties to talk about universals ever since Plato got us started on this track!

Similarly, Hare refers to “ the crude caricature of act utilitarianism which is the only version of it that many philosophers seem to be acquainted with .” Given what Bentham says about second order evils it would be a serious misrepresentation to say that he and similar act utilitarians would be prepared to punish an innocent person for the greater good.

" As Shelly Kagan says, “ Given the parameters of the actual world, there is no question that …( maximally )… promoting the good would require a life of hardship, self-denial, and austerity … a life spent promoting the good would be a severe one indeed .”

The inscription reads: “ Belonging to Ahaz ( son of ) Yehotam, King of Judah .” Given the process that created and preserved bullae, they are virtually impossible to forge.

With regard to African Americans, Gilman wrote in the American Journal of Sociology: “ The problem, is this: Given: in the same country, Race A, progressed in social evolution, say, to Status 10 ; and Race B, progressed in social evolution, say, to Status 4..

Denis MacShane, a former Foreign Office minister, said: “ Given the appalling suffering and repression of the Bahraini people, it would be a fitting gesture for the Countess of Wessex to auction these trinkets and distribute the proceeds to the victims of the regime .”

Given the Nazi predilection for “ racial purity ”, the Roma were among their first victims.

* “ Comment on Richard Schantz, ‘ The Given Regained ’”, in Philosophy and Phenomenological Research lxii ( 2001 ), 181-5

* “ Hegel and the Myth of the Given ”, in Wolfgang Welsch und Klaus Vieweg, Herausg., Das Interesse des Denkens: Hegel aus heutiger Sicht ( München: Wilhelm Fink Verlag, 2003 ), pp. 75 – 88.

Given that Unferth shows his dislike for Beowulf early in the story, Unferth ’ s choice to award Beowulf with Hrunting, which means “ thrusting ,” can be interpreted as a sign of peace and acceptance.

* Not being automatically granted the luxury of a “ diagnostic period .” Given that they know the company, COO ’ s turned CEO ’ s are often expected to hit the ground running when in actuality they too need to enter diagnostic mode to fully understand their new role and to see the Company from a new perspective.

Given the existence of important public policy goals on both sides, a city seeking to maximize walkability should not favor cul-de-sacs over grids, but should also allow some cul-de-sacs as a legitimate residential option ’ ... ‘ In addition, there are “ middle ground ” alternatives between prohibiting cul-de-sacs and mandating them.

Another partition of the given interval, Q, is defined as a refinement of the partition, P, when it contains all the points of P and possibly some other points as well ; the partition Q is said to be “ finer ” than P. Given two partitions, P and Q, one can always form their common refinement, denoted P ∨ Q, which consists of all the points of P and Q, re-numbered in order.

Given a set of data and the desire to produce some kind of “ model ” of those data ( model, in this case, meaning a function fitted through the data ), there are a variety of functions that can be chosen for the fit.

Apart from the very rare “ Kirill of Turov ’ ( even when this designation occurs, it tends to be just one of several variant readings ), the headings in ‘ his ’ manuscripts include “ Kirill the monk ,” “ Kirill the philosopher ,” ‘ Saint Kirill ,” “ The Blessed father Kirill ,” “ the blessed monk Kirill ,” “ Kirill the unworthy monk ,” “ the venerable Kirill .” Given this variety of labels, ‘ Kirill ’ s ’ texts invite several candidates for being their more likely authors ( writers whose existence has been substantiated with historical facts ).

Given that he never reigned, his brother Nicholas II is regarded as the last actual, or de facto Tsar of Russia, and Michael is relegated to a largely forgotten footnote of history.

** Given the title of Mademoiselle de Nantes after her legitimisation ;

** Given the title of Mademoiselle de Tours.

** Given the title of Mademoiselle de Blois, holding it until her marriage ;

Given that K ' ak ' Tiliw Chan Chaak was five years old when he acceded, it is most likely that his mother Lady Six Sky was de facto ruler of the Saal / Naranjo polity for some time, ruling in his name through the young king's childhood.

Given the high altitude of Val Thorens and the Glacier de Péclet the often large volume of snow means that the resort is usually open from mid-November until early May.

He suggested Hugh Massey, based on a number of puns he found incorporated in Pearl ( in addition to the " Hugo de " inscription in Cotton Nero A. x ) Given the obvious link through the name " Hugh ", Hugh Massey has been conflated with Huchoun by some academics.

Given Alfonso's maternal membership in Spain's titled aristocracy ( his mother, María de la Piedad de Yturbe y Scholtz-Hersmendorff, was the Marquesa de Belvís de las Navas, and his paternal kinship to the royal courts of Europe, the hotel quickly proved to be popular with vacationing members of Europe's social elites for its casual but discreet luxury.

Given the ethnic diversity of the city, Marbella's newspapers and magazines are published in several European languages, among which are La Tribuna de Marbella ( Spanish ), Sydkusten ( in Swedish ) and Costa del Sol Nachrichten ( in German ).

Given the failure of Walter Raleigh to establish a colony at Roanoke Island in 1584 and the successful settlement at Jamestown in 1607 and on learning that Samuel de Champlain had sailed into the St. Lawrence to initiate the settlement of New France, pressure was mounting to lay claim to the resource rich New World.

Given their sales success, it was only natural that the Coupe de Ville and Sedan de Ville were moved to their own separate series in 1959, the Series 6300, being joined by a De Ville convertible in 1964.

Given the unstable political climate during these years, Bolívar and other patriot leaders, such as Santiago Mariño, Manuel Piar, José Francisco Bermúdez and Francisco de Paula Santander often had to go into exile in the Caribbean or nearby areas of Spanish America that at the moment were controlled by those favoring independence, and from there, carry on the struggle.

Given the fact that it was an election year, whose outcome might have changed as a result of a pre-election day economic downturn, Banco de México decided to buy Mexican Treasury Securities to maintain the monetary base, thus keeping the interest rates from rising.

Given the option between touring with Helen Hayes and dancing for de Mille, he chose de Mille.

Given all the different Indian dialects, it would not be all that wrong to pronounce a more familiar sounding hi lu la hi with the suffix on the end to tag it as a settlement.

Given its inner-city roots, chicken and food is quite often ordered a la carte.

Theorem: Given A1 and A2, A3 ” and A4 ” imply A3 and A4.

Given the military-industrial requirements of the Cold War, the authors of the then secret National Security Council Report 68 ( NSC-68 ) proposed the US government undertake a massive permanent national economic expansion that would let it “ siphon off ” a part of the economic activity produced to support an ongoing military buildup to contain the Soviet Union.

Given his association with pieces of allied propaganda like the story of the “ German Corpse-Rendering Works ” ( Kadaververwertungsanstalt ) this might indicate Charteris had been behind an attempt to use the Angels for propaganda purposes.

Given this equivalence, it is valid to assume “ risk neutrality ” when pricing derivatives.

Given these considerations, many experts believe that CLOS missiles are not as ideally suited for untrained personnel use as are IR missiles, which sometimes are referred to as “ fire and forget ” missiles.

Given the great variety in Japanese armour, sashimono were used to provide a sense of “ uniform ” to the armies.

Given a drum by an “ anonymous ” benefactor, the group began having powwows.

“ Given the high incidence of craniofacial injury, appropriate safety standards for taxicabs must be initiated, including the reevaluation of the utility of the safety divider ”

Given that there is a large amount of information that needs to be processed in a short amount of time, it is advantageous to have a “ fast-track decision-making ” mechanism ( i. e., somatic markers ), that can respond rapidly in the most advantageous fashion.

The most recent measure of social dominance orientation ( see SDO-6 above ) focuses on the “ general desire for unequal relations among social groups, regardless of whether this means ingroup domination or ingroup subordination ” ( p. 312 ) Given these changes, Rubin and Hewstone believe that evidence for social dominance theory should be considered “ as supporting three separate SDO hypotheses, rather than one single theory ” ( p. 22 ).

Patient Person Given Name – find the word “ Patient ” under the UDEF object “ Person ” and find the word “ Given ” under the UDEF property “ Name ”