Thus, in the immemorial way -- in the way of the right hand that knows and the left that does not -- was the stage set for tragedy at Bari.

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

Thus the axiom of choice is not generally available in constructive set theory.

Thus, ATP was a simple request / response exchange, with no need to set up or tear down connections.

Thus flight test program was set to integrate the AARGM onto Tornado ECR's weapon system.

) Thus a set is completely determined by its elements ; the description is immaterial.

Thus the set of strings of length k in the domain is exactly the set of such strings already enumerated.

Thus the cofinality of a finite partially ordered set is equal to the number of its maximal elements.

Thus Post in his 1936 was also discounting Kurt Gödel's suggestion to Church in 1934 – 5 that the thesis might be expressed as an axiom or set of axioms.

Thus, in the important Shreveport Cases of 1914, Hughes sustained a decision of the Interstate Commerce Commission voiding intrastate rates set by the Railroad Commission of Texas.

Thus B3-34 defined a new command set, which later was used in a series of later programmable Soviet calculators.

Thus, a database and its supporting DBMS are defined here by a set of general requirements listed below.

Thus there is a natural bijection from the set of all possible equivalence relations on X and the set of all partitions of X.

Thus traditional exegesis supposes that after his release Paul sailed from Rome into Asia, passing Crete by the way, and that there he left Titus " to set in order the things that were wanting.

Thus, most security researchers set maximum times ( such as 14 days or 30 days ) before fully revealing a vulnerability to the public, since otherwise many vendors would never fix even critical vulnerabilities in their products.

Thus, variable only depends directly on variable, rather than depending on the entire set of variables.

Thus each user of an IPv6 subnet automatically has available a set of globally routable source-specific multicast groups for multicast applications.

Thus, he cautiously states: " But knowing the sure number declared by Scripture, that is six hundred sixty and six, let them await, in the first place, the division of the kingdom into ten ; then, in the next place, when these kings are reigning, and beginning to set their affairs in order, and advance their kingdom, them learn to acknowledge that he who shall come claiming the kingdom for himself, and shall terrify those men of whom we have been speaking, have a name containing the aforesaid number, is truly the abomination of desolation.

Thus many equipment manufacturers add on their own particular requirements or tighten the tolerance on a general specification to meet their particular needs ( or doing a different set of tests or using different / own testbed engine ).

Thus for each unit the seller tries to set the price equal to the consumer ’ s reservation price.

Thus, they capture the idea of function composition within a set.

Thus its range of action was predominantly set in Italy and France, where such sects had settled.

Thus, a set of input objects is gathered and corresponding outputs are also gathered, either from human experts or from measurements.

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

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, the dotted line shown in figure 4 was taken as typical for the temperature distribution for all blowing rates.

Thus it follows that the secants of **zg are all invariant.

Thus Af where the maximization is over all admissible policies Af, and Af is related to Af by ( 5 ).

Thus creativity may run all the way from making a cake, building a chicken coop, or producing a book, to founding a business, creating a League of Nations or, developing a mature character.

Thus all differences were leveled, and all contrasts erased, in a realm of no distinction, and the harmonious balance of the Lo Shu square could effectively symbolize the world in balanced harmony around a powerful central axis.

Thus we hear of abbots going out to hunt, with their men carrying bows and arrows ; keeping horses, dogs and huntsmen ; and special mention is made of an abbot of Leicester, c. 1360, who was the most skilled of all the nobility in hare hunting.

Thus Christ's atonement is intended for all, but requires faith to be effected.

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

Thus she, through whom salvation was being prepared for all people, would be the first to receive the promised fruit of salvation.

Thus, during the abdication crisis of 1936, caused by Edward VIII's desire to marry Wallis Simpson, the consent of all realms concerned, along with, in some cases, new acts of parliament, was required in Britain and throughout the British Dominions to allow for Edward's stepping aside and to ensure that if he had any children they would have no claim to the thrones.

Thus, in Steiner's view, we can overcome the subject-object divide through inner activity, even though all human experience begins by being conditioned by it.

Thus, anthroposophy considers there to be a being who unifies all religions, and who is not represented by any particular religious faith.

Thus a third style, the " curved lip " style was produced, and all official and third-party cartridges during the console's lifespan were released ( or re-released ) using this style.

Thus, all the antiderivatives of x < sup > 2 </ sup > can be obtained by changing the value of C in F ( x ) = ( x < sup > 3 </ sup >/ 3 ) + C ; where C is an arbitrary constant known as the constant of integration.

Thus there are alignments in all directions which would suggest there is little of astronomical significance, However, ethnohistorical records show that the various directions do have cosmological and astronomical significance with various points in the landscape being significant at different times of the year.

Thus, current expected inflation reflects a weighted average of all past inflation, where the weights get smaller and smaller as we move further in the past.

Thus, the energy required to break any single pair is related to the energy required to break all of the pairs ( or more than just two electrons ).

Thus the electrons stay paired together and resist all kicks, and the electron flow as a whole ( the current through the superconductor ) will not experience resistance.

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, a player should use Blackwood only when he can ascertain that the partnership holds at least second-round controls in all suits ( kings or, if a suit fit is found, singletons ).

Thus, all carbon isotopes have nearly identical chemical properties because they all have six protons and six electrons, even though carbon atoms may differ in number of neutrons.