Thus, we should prioritize social reform over attempts to account for consequences, individual virtue or duty ( although these may be worthwhile attempts, provided social reform is provided for ).

Thus, contrary to the first impression its name might convey, and as realized in specific approaches and disciplines ( e. g. Fuzzy Sets and Systems ), intuitionist mathematics is more rigorous than conventionally founded mathematics, where, ironically, the foundational elements which Intuitionism attempts to construct / refute / refound are taken as intuitively given.

Thus, there have been several theories and attempts to quantify risks.

Thus a conservative classification of Sino-Tibetan / Tibeto-Burman would posit several dozen small coordinate families and isolates ; attempts at subgrouping are either geographic conveniences or hypotheses for further research.

" Thus, sabermetrics attempts to answer objective questions about baseball, such as " which player on the Red Sox contributed the most to the team's offense?

Thus, the United States entered into a ten-year war in Vietnam, taking over from French colonialists, and supported Portugal in its attempts to hold on to Angola.

Thus, the first modern rounding of the cape in 1488 by Portuguese explorer Bartolomeu Dias was a milestone in the attempts by the Portuguese to establish direct trade relations with the Far East ( although in his histories Herodotus proves, disbelievingly, that some Phoenicians had done so far earlier than this ).

Thus, Barovia's vampire lord Strahd von Zarovich's many attempts to win back his love, Tatyana, are doomed to failure, but the Dark Powers arrange such that he never truly loses hope.

Thus a British assault on Sullivan's Island was driven off and Clinton then abandoned his attempts to capture the city.

Thus both the Pattern and Logrus are forestalled for a time, in their attempts to escalate their conflict: while Corwin begins the journey back to Amber, Merlin-who wants peace with Amber-returns to Chaos to await his coronation.

Thus Bloom attempts to work out the process by which the small minority of ' strong ' poets manage to create original work in spite of the pressure of influence.

Thus, his structuralist theorizing became another exercise in his ongoing attempts to dissect and expose the misleading mechanisms of bourgeois culture.

Thus a balance must be reached that attempts to achieve both goals whilst not compromising either too much by doing so.

Thus if the shooter attempts to hit the level distance R, s / he will actually hit the slant target.

Thus, Deleuze attempts to argue that Masochism and Sadism arise from such different impulses that the combination of the two terms is meaningless and misleading.

Thus, ultimately the defeat marked the end of Byzantine attempts to recover the Anatolian plateau, which was now lost to the empire forever.

Thus the individual islands resisted British attempts at closer union.

Thus, if actions arise so that the self attempts self-explanation, confusion may well occur within linguistic mental pathways and processes.

Thus two manifestations, one individual, and the other collective, amongst Southern nation-states, existed in their attempts to generate reform.

Thus the notorious practice of clandestine Fleet Marriages associated with London ’ s Fleet Prison was ended, although there were various short-lived and abortive attempts to claim exemption for the Savoy Chapel in the Strand and the parish of Temple in Cornwall.

Thus, it attempts to be as authentic as possible given the realities of modern life.

Thus, Shun survived many attempts on his life.

Thus, rare organisms like Chloroflexus aurantiacus that can survive using either respiration or photosynthesis are of interest in on-going attempts to trace the evolution of photosynthesis.

Thus, an axiom is an elementary basis for a formal logic system that together with the rules of inference define a deductive system.

Thus we cannot define being, unity and similar concepts.

Thus users can recognize the abnormality of a weather situation without having to define specific space-and time-dependent thresholds.

Thus modernism, which had been a minority taste before the war, came to define the 1920s.

Thus the welfare analysis of oligopolies is sensitive to the parameter values used to define the market's structure.

Thus, Melnyk's rebuttal, stated very crudely, is that one should define physicalism in relation to current physics, and hold a similar attitude towards its truth as most scientists hold towards the truth of currently accepted scientific theories.

Thus an RGB value does not define the same color across devices without some kind of color management.

Thus, short story writers may define their works as part of the artistic and personal expression of the form.

Thus, to define particle trajectories, one needs an additional rule that defines which space-time points should be considered instantaneous.

Thus there is an infinite list of English phrases ( where each phrase is of finite length, but lengths vary in the list ) that unambiguously define real numbers ; arrange this list by length and then dictionary order, so that the ordering is canonical.

Thus some prior information of the geometry is needed to define the correct normal direction.

Thus one can define a ( unique ) unitary group of dimension n for the extension F < sub > q² </ sub >/ F < sub > q </ sub >, denoted either as U ( n, q ) or U ( n, q² ) depending on the author.

Thus, the global perception of what can define world music has evolved to include a contemporary feature, and is only contradicting in proportion to one's adherence to world music in its classic context.

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 a covering map p: C → X defines a conjugacy class of subgroups of π < sub > 1 </ sub >( X, x ) and one can show that equivalent covers of X define the same conjugacy class of subgroups of π < sub > 1 </ sub >( X, x ).

Thus one could choose to define all voltage differences relative to some other standard, rather than the Earth, resulting in the addition of a constant offset.

Thus we define the representations of G on an Hilbert space H to be those group homomorphisms, ρ, which arise from continuous actions of G on H. We say that a representation ρ is unitary if ρ ( g ) is a unitary operator for all g ∈ G ; i. e., for all v, w ∈ H. ( I. e.

Thus, in Euclidean geometry three non-collinear points determine a circle ( as the circumcircle of the triangle they define ), but four points in general do not ( they do so only for cyclic quadrilaterals ), so the notion of " general position with respect to circles ", namely " no four points lie on a circle " makes sense.

Thus it is more correct to define the status of Hungary as autonomous, rather than independent.

Thus, one may define the quotient category hComp or K, the homotopy category of chain complexes.

Thus, by maximizing the entropy over a suitable set of probability distributions on X, one finds the distribution that is least informative in the sense that it contains the least amount of information consistent with the constraints that define the set.

Thus no L-formula True ( n ) can define T *.

Thus the number of quantifier alternations required to define a set gives a measure of the complexity of the set.

Thus, we would say that two different points define a line and a decomposition of this line into the disjoint union of an open segment and two rays.