Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus there is a clearer division of authority, administrative and legislative.

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, there is an added incentive to stay on the job.

Thus there are polynomials Af such that Af.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus it is reasonable to believe that there is a significant difference between the two groups in their performance on this task after a brief `` structuring '' experience.

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 there was really an excess of eighteenth-century charm as one of these light-weight pieces followed another on Saturday night.

Thus although most species in the order are herbaceous, some no more than 15 cm high, there are a number of climbers ( e. g. some species of Asparagus ), as well as several genera forming trees ( e. g. Agave, Cordyline, Yucca, Dracaena ), some of which can exceed 10 m in height.

Thus the negation of the axiom of choice states that there exists a set of nonempty sets which has no choice function.

Thus, before the modern assembly line took shape, there were prototypical forms in various industries, as outlined below.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

Thus, almost all positive integers are composite ( not prime ), however there are still an infinite number of primes.

" Thus Ambrose refused to be drawn into a false conflict over which particular local church had the " right " liturgical form where there was no substantial problem.

Thus, there is no assault if an ox gores a man.

Thus he maintained that there must be blackness as well as whiteness in snow ; how otherwise could it be turned into dark water?

Thus, if every historian were to claim that there was a solar eclipse in the year 1600, then though we might at first naively regard that as in violation of natural laws, we'd come to accept it as a fact.

According to the Christian doctrine of Universal Reconciliation, the Greek New Testament scriptures use the word " eon " to mean a long period ( perhaps 1000 years ) and the word " eonian " to mean " during a long period "; Thus there was a time before the eons, and the eonian period is finite.

Thus, there was seen a need for a new law that would ensure the continuance of the succession following the death of the last legal heir under the Bill of Rights, being Princess Anne, guaranteeing the line of succession would continue in the Protestant line, and excluding any possible claims by the deposed James II or his son and daughter, James Francis Edward and Louisa Maria Teresa Stuart.

Thus, services could be moved to a different machine and, so long as they kept the same service name, there was no need for users to do anything different to continue accessing the service.

This latter construal is sometimes expressed by saying " there is no fact of the matter as to whether or not P ." Thus, we may speak of anti-realism with respect to other minds, the past, the future, universals, mathematical entities ( such as natural numbers ), moral categories, the material world, or even thought.

Thus, the Comte de Paris is presently the Orléanist pretender to the French throne.

Thus, she charged Dr. Chull Soon Yim to succeed her as the fourth chancellor of CAU, and cultivate the university into a world-class institution in accordance with the ideal philosophies for which had presently strived.

Thus emboldened, he grandiosely speaks of the greatness of his party, the Potterbills, presently in power, but also losing ground to the villainous opposition party, the Rotterjacks.

Thus Russell's example, " The present king of France exists ", is neither true nor false, since France is not presently a monarchy, and therefore " the present king of France " does not designate ; whereas " Napoleon exists " is simply false, since although Napoleon once existed, the moment he died he took on the property of nonexistence.

Thus, designation of a National Natural Landmark presently constitutes only an agreement with the owner to preserve, insofar as possible, the significant natural values of the site or area.

By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.

Thus for a limit ordinal, there exists a δ-indexed strictly increasing sequence with limit α.

Thus, in the sentence " There exists a man ", the term " man " is asserted to be part of existence.

Thus if we reason from the statement " Pegasus flies " to the statement " Pegasus exists ", we are not asserting that Pegasus is made up of atoms, but rather that Pegasus exists in a particular worldview, the worldview of classical myth.

Thus the cache that exists on the International Space Station, GC1BE91, uses the launch area Baikonur in Kazakhstan as its position.

Thus the difference between the two definitions of real numbers can be thought of as the difference in the interpretation of the statement " for all ... there exists ..."

Thus the past, present, future, and anything in and of, would simply exists without possible creation of, or deviation from.

Thus we can conceive of a “ noumenal ” world ( noumenal meaning " object of thought ") which exists only as a heuristic for our cognitive capacities and not as something directly accessible to experience.

Thus panentheism separates itself from pantheism, positing the extra claim that God exists above and beyond the world as we know it.

Thus, " The present king of France " is analyzed, according to Russell's theory of descriptions, as " There exists an individual who is currently the king of France, there is only one such individual, and that individual is bald.

if there exists an integer such that .< ref > Thus, divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors.

Thus scientific laws while somewhat idealized have more to do with describing sensations than with reality as it exists beyond sensations.

Thus Koons concludes that the problem of theodicy ( explaining how God can be good despite the apparent contradiction presented in the problem of evil ) does not pose a challenge to all possible forms of theism ( i. e., that the problem of evil does not present a contradiction to someone who would believe that God exists but that he is not necessarily good ).

Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system even though it does not exist for each photon.

Thus, matter exists for the sake of receiving its form, and an organism has sight for the sake of seeing.

Thus, there exists a statistically significant imbalance between the frequency of sudden stratospheric warmings if these events are grouped according to the QBO phase ( easterly or westerly ).

Thus, the ' pataphor has created a world where the chessboard exists, including the characters who live in that world, entirely abandoning the original context.

Thus, there is no one person responsible for verifying that any one particular loan is sound, that the assets securing that one particular loan are worth what they are supposed to be worth, that the borrower responsible for making payments on the loan can read and write the language that the papers that he / she signed were written in, or even that the paperwork exists and is in good order.

Thus, due to the painstaking labour of these musicians and researchers, there now exists a stable and definitive collection of Thyagaraja's music.

Thus the cervical nerves are numbered by the vertebra below, except C8, which exists below C7 and above T1.

Thus ZF together with " there exists a weakly inaccessible cardinal " implies that ZFC is consistent.

Thus, many speakers do not differentiate between the vowel sounds ( as in " dress ") and ( as in < trap >), except in cases where a minimal pair such as < bed >/< bad > exists in the vocabulary of the speaker.

Thus, a C < sup > 1 </ sup > function is exactly a function whose derivative exists and is of class C < sup > 0 </ sup >.