Thus far the advances made have been almost entirely along functional lines.

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

Thus, OR1 and OR2 are almost always simultaneously occupied by cI.

Thus, while there was a good measure of debate in the Early Church over the New Testament canon, the major writings are claimed to have been accepted by almost all Christians by the middle of the 3rd century.

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

Thus, reasoned Oort, a comet could not have formed while in its current orbit, and must have been held in an outer reservoir for almost all of its existence.

Thus if an event or its complement almost surely occurs, it is independent of itself.

Thus, while it is hypothesized to exist and comprise the vast majority of matter in the universe, almost all of its properties are unknown and a matter of speculation, because it has only been observed through its gravitational effects.

Thus, an order for opium tincture containing directions in teaspoons is almost certainly in error.

Thus, when hyperthyroidism is confirmed, or when blood results are inconclusive, thyroid antibodies should be measured ( almost all patients with Graves ' hyperthyroidism have detectable TSHR-Ab levels ).

Thus, the new definition of trademark in India broadly encompasses almost all the elements of trade dress under the US law.

Thus, almost no Soviet employees or managers had firsthand experience with decision-making in the conditions of a market economy.

Thus, appointing Murphy would almost certainly cost the ALP a Senate seat at the next half-Senate election.

Thus they can be placed behind enemy lines, and have the capability to deploy almost anywhere with little warning.

Thus, English names for creatures not native to Great Britain are almost always loanwords.

Thus almost the entire navy was caught unprepared and captured without resistance, and all the men taken were put to death.

Thus a thin 2-dioptre lens placed close to a thin 0. 5-dioptre lens yields almost the same focal length as a 2. 5-dioptre lens would have.

Thus, if leadership amounts to getting the greatest number of followers, then among the bonobos, a female almost always exerts the strongest and most effective leadership.

Within the class P, however, polynomial-time reductions are inappropriate, because any problem in P can be polynomial-time reduced ( both many-one and Turing ) to almost any other problem in P. Thus, for classes within P such as L, NL, NC, and P itself, log-space reductions are used instead.

Thus, almost any telephone on a military base could be direct-dialed via AUTOVON.

Thus, although the Fynbos comprises only 6 % of the area of southern Africa, it has half the species on the subcontinent – and in fact has almost 1 in 5 of all plant species in Africa.

Thus, in Antioquia, the natives disappeared almost completely.

The overman ( Übermensch ), a self-mastered individual who has achieved his full power, is an almost omnipresent idea in Thus Spoke Zarathustra.

Thus, Scofield's premilliennialism seemed almost prophetic.

Thus, the task is to find universal properties that uniquely determine the objects of interest.

Thus if we wish to claim that no-cloning is a uniquely quantum result, some care is necessary in stating the theorem.

Thus rather than " nurture ", behavior geneticists distinguish shared family factors ( i. e., those shared by siblings, making them more similar ) and nonshared factors ( i. e., those that uniquely affect individuals, making siblings different ).

Thus was Darnley's uniquely ' British ' inheritance put to use at last ... The subsequent release of Darnley into Scotland and the restoration of his father at the Scottish Court were part of this policy: the political disaster of the Darnley marriage as yet unforeseen.

Thus, Kolmogorov introduced a second hypothesis: for very high Reynolds numbers the statistics of small scales are universally and uniquely determined by the viscosity () and the rate of energy dissipation ().

Thus, every element of Dic < sub > n </ sub > can be uniquely written as a < sup > k </ sup > x < sup > j </ sup >, where 0 ≤ k < 2n and j = 0 or 1.

Thus closed system thermodynamics can be used to evaluate functions of state for open systems, but processes specified in terms of heat and work transfer are not physically uniquely defined for open systems.

Thus every rotation can be represented uniquely by an orthogonal matrix with unit determinant.

Since any vector v is a linear combination ∑ v < sup > j </ sup > e < sub > j </ sub > of its components, df is uniquely determined by df < sub > p </ sub >( e < sub > j </ sub >) for each j and each p ∈ U, which are just the partial derivatives of f on U. Thus df provides a way of encoding the partial derivatives of f. It can be decoded by noticing that the coordinates x < sup > 1 </ sup >, x < sup > 2 </ sup >,... x < sup > n </ sup > are themselves functions on U, and so define differential 1-forms dx < sup > 1 </ sup >, dx < sup > 2 </ sup >, ..., dx < sup > n </ sup >.

Thus, according to the Cutlerites, whereas the church can never exist without the priesthood ( a belief held by practically all other Latter Day Saint churches ), the priesthood can exist on earth without the church ( a uniquely Cutlerite belief ), as it did between 1829 and 1830.

Thus, the first two results appeared to establish 11 dimensions uniquely, the third result appeared to specify the theory, and the last result explained why the observed universe appears to be four-dimensional.

Thus, during the Nazi invasion and occupation of Kalmykia in 1942, German forces uniquely found volunteers among the Kalmyks for the Kalmykian Voluntary Cavalry Corps, which killed many Soviet partisans.

Thus subverting Harley's theory that mapping is uniquely a source of power for the powerful.

Thus, as it uniquely illustrates the articles ' discussion of the artist's representation of the subjects, it is not replaceable by the public domain image.

Thus an inhabitant of Brazil should have become known in Portuguese as a Brasiliano (" Brazilian "), but uniquely among Portuguese demonyms they are instead referenced as a Brasileiro (" Braziler ").

The Cantor – Bendixson theorem states that closed sets of a Polish space X have the perfect set property in a particularly strong form ; any closed set C may be written uniquely as the disjoint union of a perfect set P and a countable set S. Thus it follows that every closed subset of a Polish space has the perfect set property.

Thus, as he saw it ( in Comparative Studies in Vaishnavism and Christianity ), Vaishnavism and Christianity were two distinct religious traditions, each with its own uniquely rich tradition of historical exegesis that spanned two millennia and could in no way be seen as being phases in the development of ( a Eurocentric ) human civilization, as one leading to another in a pattern of cause and effect.