Given the conceptual context within which ancient thought thrived, how could anyone have questioned this principle??

Given the cosmological principle, Hubble's law suggested that the universe was expanding.

The wavelets forming a continuous wavelet transform ( CWT ) are subject to the uncertainty principle of Fourier analysis respective sampling theory: Given a signal with some event in it, one cannot assign simultaneously an exact time and frequency response scale to that event.

Given that controls are imperfect, strong physical security applies the principle of defense in depth using appropriate combinations of overlapping and complementary controls.

Given a condition number, the relative error of compensated summation is effectively independent of n. In principle, there is the O ( nε < sup > 2 </ sup >) that grows linearly with n, but in practice this term is effectively zero: since the final result is rounded to a precision ε, the nε < sup > 2 </ sup > term rounds to zero unless n is roughly 1 / ε or larger.

Given the electromechanical principle of the meter, the deviation of the needle is actually approximately proportional to the average of the part of the signal with more than approximately 0. 4V instantaneously because of the two copper-oxide rectifiers always in series, which transfer function curve has a knee around 0. 2V.

" Given the gift of this " divinization " in grace, " a new principle of energy ," and with the support of " Christ's family ," the Church, Escrivá states that the difficult ideal of becoming a saint, another Christ, is " also easy.

Euclid poses the problem: " Given two numbers not prime to one another, to find their greatest common measure ".

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

Given that one cannot be motivated by reason alone, requiring the input of the passions, Hume argued that reason cannot be behind morality.

Given the limited success of the Charity School, however, Wheelock intended his new College as one primarily for whites.

Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has

Given good circumstances one might be able to discern the result of some human activity such as the changing of the Netherlands ' coast or the partial drying out of the Aral Sea, but even that would not be easy.

Given the existence of a Godlike object in one world, proven above, we may conclude that there is a Godlike object in every possible world, as required.

Given our formula φ, we group strings of quantifiers of one kind together in blocks:

Given an equilateral triangle, the counterclockwise rotation by 120 ° around the center of the triangle " acts " on the set of vertices of the triangle by mapping every vertex to another one.

Given a general algorithm for integer factorization, one can factor any integer down to its constituent prime factors by repeated application of this algorithm.

Given a complete set of axioms ( see below for one such set ), modus ponens is sufficient to prove all other argument forms in propositional logic, and so we may think of them as derivative.

Given significant distance from the magnetic poles, one can figure which hand is which using a magnetic compass and the sun.

Given two secondary stations, the time difference ( TD ) between the primary and first secondary identifies one curve, and the time difference between the primary and second secondary identifies another curve, the intersections of which will determine a geographic point in relation to the position of the three stations.

Given the same set of verifiable facts, some societies or individuals will have a fundamental disagreement about what one ought to do based on societal or individual norms, and one cannot adjudicate these using some independent standard of evaluation.

Given an arithmetic function, one can generate a bi-infinite sequence of other arithmetic functions by repeatedly applying the first summation.

Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.

Given the above fact, one can ask:

Given a preorder on S one may define an equivalence relation ~ on S such that a ~ b if and only if a b and b a.

# Given any two distinct points, there is exactly one line incident with both of them.

# Given any two distinct lines, there is exactly one point incident with both of them.

# Given an array of values to be sorted, set up an auxiliary array of initially empty " pigeonholes ," one pigeonhole for each key through the range of the original array.

Given the unusual casting and production demands, Pacific Overtures remains one of the least-performed musicals by Stephen Sondheim.

Given the above expression, evidently the result of her ( local ) measurement is that the three-particle state would collapse to one of the following four states ( with equal probability of obtaining each ):

Given the proposition that ' a persons life prospects should not be decided by factors outside of their control or for which a person cannot claim personal credit ' ( i. e. social status, inherited wealth, race and other accidents of birth ) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just.

Given that the validity of conclusions drawn from a statistical analysis depend on the validity of any assumptions made, it is clearly important that these assumptions should be reviewed at some stage.

Given the date of his publication and the widespread, permanent distribution of his work, it appears that he should be regarded as the originator of the concept of space sailing by light pressure, although he did not develop the concept further.

Given how little we can know for sure, our focus should be on this earth and life ; beauty, justice, love.

Given an ongoing rift in the sport during the 1860s between the northern professionals and Surrey, MCC feared the loss of its authority should Grace " throw in his lot with the professionals " so it was considered vital for them and their interests to get him onside.

Given his socialist agenda in Egypt, the Ba ' ath should have been his natural ally, but Nasser was hesitant to share power.

Given the sensitivity of STEREO's COR2 coronagraph, anything larger than in diameter should have been detected.

Given these inconsistencies, the role of ultrasound in the treatment of CTS is debatable and it should be considered an experimental treatment.

Given these assumptions, the following forces should be taken into account:

Given an adequate supply of food, larvae should pupate and weave a silken cocoon within 1 – 2 weeks after 3 larval stages.

Given that " production could be carried on without any organization is, firm at all ", Coase asks, why and under what conditions should we expect firms to emerge?

Given that the absolute vorticity is positive ( negative ) in the Northern ( Southern ) hemisphere, the threshold value should be taken as positive ( negative ) north ( south ) of the equator.

Given the associated safety risks, the TGA concluded " efforts should be made to curb the illegal availability of colloidal silver products, which is a significant public health issue.

Given this connection, she suggests the major war should have been called " The Great Cheyenne War ".

Given that the plants above ground are readily distinguishable, and chiefly because their habitats rarely overlap, it is unlikely that the toxic plant's root should be found beneath the foliage of the edible one's.

Given the general rule in British law that a wife automatically takes her husband's rank upon marriage, Mrs Simpson consequently should have been addressed, upon marriage to the duke, as Her Royal Highness.

Given the death of Princess Charlotte without surviving children, should the Ord or Lowe links be substantiated, the line descended through them would join a large number of claimed surviving descendants of King George IV.

Given the prevalence of childhood sexual abuse, even if only a small proportion are repressed and only some of them are subsequently recovered, there should be a significant number of corroborated cases.

Given that reasoning, Jones and several members argued that the group should commit " revolutionary suicide " by drinking cyanide-laced grape flavored Flavor Aid ( not Kool-Aid despite the popular phrase ).

Given that the endgame ( yose ) contains fewer possible moves than the opening ( fuseki ) or middle game, one could suppose that it was easier to play, and thus that computers should be easily able to tackle it.

* Given the weight of the train and the gradients on the line, both brake-vans should have been at the rear of the train

Given Weyoun's untrustworthy nature, it is unclear which information should be believed.

Given the intense lightning activity at Jupiter, the Schumann resonances should be easily detectable with a sensor suitably positioned within the planetary-ionospheric cavity.

Given research in cognitive psychology, some educators believe that schools should focus on teaching their students critical thinking skills and cultivation of intellectual traits.