Thus, Judaism rejects the notion that anyone can or should die for anyone else's sin.

Thus, the only logical possibilities are to accept non-Euclidean geometry as physically real, or to reject the entire notion of physical tests of the axioms of geometry, which can then be imagined as a formal system without any intrinsic real-world meaning.

Thus another approach is to incorporate the notion of suffering into the definition.

Thus, the challenge is to create agile or discovery-driven implementations of the EVM principle, and not simply to reject the notion of measuring technical performance objectively.

Thus, for example, around 60 manuscripts are extant containing Welsh-language versions of the Historia, the earliest of which were created in the 13th century ; the old notion that some of these Welsh versions actually underlie Geoffrey's Historia, advanced by antiquarians such as the 18th-century Lewis Morris, has long since been discounted in academic circles.

Thus three major themes in 19th century mathematics were combined by Lie in creating his new theory: the idea of symmetry, as exemplified by Galois through the algebraic notion of a group ; geometric theory and the explicit solutions of differential equations of mechanics, worked out by Poisson and Jacobi ; and the new understanding of geometry that emerged in the works of Plücker, Möbius, Grassmann and others, and culminated in Riemann's revolutionary vision of the subject.

Thus, null sets may be interpreted as negligible sets, defining a notion of almost everywhere.

Thus, in place of God's role as guarantor of the coherence of the world, Kant posits a faculty of reason structured by the forms of our intuition ( our sense of time and space ) and the categories of our understanding ( like the notion of cause and effect ).

Thus, lineally and geopolitically, Bruce attempted to support his anticipated notion of a pan-Gaelic alliance between Scottish-Irish Gaelic populations, under his kingship.

Thus, justification is a normative notion.

Thus, he developed his notion of hamartia, or tragic flaw, which was really an error in judgment by the main character or protagonist.

There is no sustained, mature analysis of the notion ..." Thus, some critics object, it would be acceptable to torture one person if this would produce an amount of happiness in other people outweighing the unhappiness of the tortured individual.

Thus, in a sense, the notion of a Noetherian ring unifies the ideal structure of various " natural rings ".

Thus, the general notion of a statistical ensemble with nearest-neighbor interactions leads to Markov random fields, which again find broad applicability ; for example in Hopfield networks.

Thus, in the West, the notion of ethnicity, like race and nation, developed in the context of European colonial expansion, when mercantilism and capitalism were promoting global movements of populations at the same time that state boundaries were being more clearly and rigidly defined.

Thus, nationalism is invoked in conscience to quell tribal conflict and the notion of a Brotherhood of Man is invoked to quell national conflicts.

Thus, it encouraged biological fathers to reject not only the notion of an obligation to marry the mother but also the very idea of a paternal obligation.

Thus, he described his notion of an esoteric philosophy which referenced the eternal truth or wisdom which lies at the heart of all traditions as a " science of reality " based on the method of " certain demonstration " ( al-burhan al-yaqini ).

Thus, the notion that the Trinity consists of " Three persons in one God " is not a part of Latter-day Saint beliefs.

Thus Kant presents the notion of the hypothetical Kingdom of Ends of which he suggests all people should consider themselves both means and ends.

Thus if we set aside the notion of standardization, I believe it would be more appropriate to speak of 25 languages derived from Old Tibetan.

Thus the Governor-General hit upon the notion to name the outpost Nueva ( meaning new Ecija ). Both the New and Old Ecija were washed by navigable rivers-the former, by Rio Grande de Pampanga and the latter, by the river Genil.

The notion is closely related to the idea of a multiplicative character in group theory, which is a homomorphism χ from a group G to the multiplicative group of a field F. Thus χ: G → F < sup >×</ sup > satisfies χ ( e ) = 1 ( where e is the identity element of G ) and

Thus weights are primarily of interest for abelian Lie algebras, where they reduce to the simple notion of a generalized eigenvalue for space of commuting linear transformations.

Thus we are compelled to face the urbanization of the South -- an urbanization which, despite its dramatic and overwhelming effects upon the Southern culture, has been utterly ignored by the bulk of Southern writers.

Thus with regard to the loss of tradition, in the change from order to disorder the metaphysics of change works itself out as a disruption of the individual soul, a change in which man continues as an objective ontological existent, but no longer as a man.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus Trevelyan repeats the story which pictured Victor Emmanuel as refusing to abandon the famous Statuto at the insistence of General Radetzky.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the government simultaneously undertook the vast burden of social security which had traditionally been privately discharged, and created a national scarcity which has engendered calamitous problems of social security.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, there has come into being a situation in which the state must raise all of its own revenues and, in addition, must give assistance to its local governments.

Thus, in the last few years, a number of programs which looked very promising at the time their development was commenced have since been completely eliminated.

Thus was invented the single thread sewing machine, which Mr. Gibbs in partnership with Mr. Willcox decided to bring to Brown & Sharpe with the proposal that the small company undertake its manufacture.

Thus, direct comparisons can be drawn with free burning arcs which have been studied in detail during the past years and decades by numerous investigators ( Ref. 3 ).

Thus the Af are projections which correspond to some direct-sum decomposition of the space V.

Thus Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.

Thus in a context in which there has been discussion of snow but mention of local conditions is new, dominant stress will probably be on here in it rarely snows here, but in a context in which there has been discussion of local weather but no mention of snow, dominant stress will probably be on snows.

Thus in Mary wrote an account of the trip first strong stress on Mary marks Mary as the first in a series of people who wrote accounts of the trip, strong stress on wrote marks the writing as the first of a series of actions of Mary's concerned with an account of her trip ( about which she may later have made speeches, for example ), and strong stress on trip makes the trip the first of a series of subjects about which Mary wrote accounts.

Thus, besides the training provided to youth in school, the existence of the school program can have supplementary benefits to industry which make it an asset to industrial development efforts.

Thus far, the cases which have come before the courts have involved only the issue of referral where the job is vacant due to a strike -- condition ( 1 ) in the Regulation of the Secretary.

Thus, when specifically permitted, the operand of a given line on the Autocoder coding sheet may be continued in the operand of from one to four additional lines which immediately follow.

Thus, when Dartmouth's Winter Carnival -- widely recognized as the greatest, wildest, roaringest college weekend anywhere, any time -- was broadcast over a national television hookup, Prexy John Sloan Dickey appeared on the screen in rugged winter garb, topped off by a tam-o'-shanter which he confessed had been acquired from a Smith girl.

Thus some provinces contained tribes which detested each other, and to them independence meant an opportunity for war.

Thus the image of God is that which makes a man a man and not an oyster ; ;

Thus, a well-planned adobe wall of the appropriate thickness is very effective at controlling inside temperature through the wide daily fluctuations typical of desert climates, a factor which has contributed to its longevity as a building material.