Thus the Kol Nidre was discredited in both of the Babylonian academies and was not accepted by them.

Thus they reproached him because he wrote in Hebrew instead of in the customary Talmudic idiom, because he departed from the Talmudic order and introduced a division and arrangement of his own, and because he dared to sometimes decide according to the Tosefta and the Jerusalem Talmud as against the Babylonian Talmud.

Thus the French kings are a good example of a non-imperial Catholic monarchy that was rather successful in getting a great say in the French Catholic Church ( such as commendatory prelatures ) and getting access to significant income from the Church's property ; during and around the ' Babylonian Exile ' of the papacy in Avignon they even had a heavy hand in the papacy as such ; and aspects of Gallicanism reflect the desire to give even the liturgy ( even when Latin was the only language for liturgical ritual in the Latin Rite ) a distinctive French flavour.

Thus, the day of the Lord is about God chastening his people, whether it be through the Babylonian invasion of Jerusalem or a locust plague described in Joel 2: 1-11.

Thus the first grouping could be the initial waxing to David, the next fourteen the waning to the Babylonian captivity and the last period the waxing towards Jesus.

Thus, the vast majority of historians and archaeologists view Babylonian chronology back to 747 BC as settled.

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

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, 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 the actual mathematics of mathematical games may not be apparent to the average player.

Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same.

Thus, formalism need not mean that mathematics is nothing more than a meaningless symbolic game.

Thus, in order to show that any axiomatic system of mathematics is in fact consistent, one needs to first assume the consistency of a system of mathematics that is in a sense stronger than the system to be proven consistent.

Thus, when doing mathematics, we can see ourselves as telling a sort of story, talking as if numbers existed.

Thus Grosseteste concluded, following very much in what Boethius had argued, that mathematics was the highest of all sciences, and the basis for all others, since every natural science ultimately depended on mathematics.

Thus, while Fessenden was only a teenager, he was teaching mathematics to the young children at the school while simultaneously studying with the older students at Bishop's University.

Thus Hilbert is insisting that mathematics is not an arbitrary game with arbitrary rules ; rather it must agree with how our thinking, and then our speaking and writing, proceeds :".

Thus, providing students of archaeology with a solid background in quantitative sciences such as mathematics, statistics and computer sciences seems today more important than ever.

Thus, inverse problems are one of the most important, and well-studied mathematical problems in science and mathematics.

Thus in 1900 he enrolled to École Normale Supérieure to study mathematics.

Thus the root of mathematics and scientific pursuits in Pythagoreanism is also based on a spiritual desire to free oneself from the cycle of birth and death.

Thus the order of arguments in some of the constructions below is exactly the opposite from those in many mathematics textbooks.

Thus humans do not invent mathematics, but rather discover and experience it, and any other intelligent beings in the universe would presumably do the same.

Thus the rationalists took mathematics as their model for knowledge, and the empiricists took the physical sciences.

Thus Kant arrives at the conclusion that all pure mathematics is synthetic though a priori ; the number 7 is seven and the number 5 is five and the number 12 is twelve and the same principle applies to other numerals ; in other words, they are universal and necessary.

Thus Bardas founded the Magnaura School with seats for philosophy, grammar, astronomy and mathematics, supported scholars like Leo the Mathematician and promoted the missionary activities of Cyril and Methodius to Greater Moravia.

In mathematics, a P-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their k-th power for 1 ≤ k ≤ P. Thus, a magic cube is bimagic when it is 2-multimagic, and trimagic when it is 3-multimagic, tetramagic when it is 4-multimagic.

Thus the overall ratios of the three coinages remained roughly equivalent.

Thus, this notion, which remained relevant throughout Chinese history, reflects the order of nature.

Thus, they initially opted for project approval and censorship guidelines while leaving what remained of the industry in private hands.

Thus, when World War II broke out in September 1939, Greece remained neutral.

Thus, Alexander remained in command of the 15th Army Group, and, with the support of numerous allied commanders, controversially authorised the bombing of the historic abbey at Cassino, which resulted in little advance on the German Winter Line defences.

Thus encouraged, the encircling regiments remained in place, maintaining continual pressure, until weakened British dispositions enabled the host to make a final surge forward.

Thus, Peter Wimsey remained forever fixed on the background of inter-war England, and the books are nowadays often read for their evocation of that period as much as for the intrinsic detective mysteries.

Thus the Mary Rose was subject to salvage from the sixteenth century and later, but a very large amount of material, buried in the sediments, remained to be found by maritime archaeologists of the twentieth century.

Thus, Romania was created as a personal union, albeit a Romania that did not include Transylvania, where the upper class and the aristocracy remained mainly Hungarian, although Romanian nationalism inevitably ran up against Hungarian nationalism at the end of the 19th century.

Thus Lenin remained the enfant terrible of the Russian Social Democratic Labour Party, although in this point in the war his following in Russia was as little as 10 000 and he must have seemed no more than the leader of an extremist wing of a bankrupt organization.

Thus, Wimbledon, the US Open, the French Open, and the Australian Open ( dating to 1905 ) became and have remained the most prestigious events in tennis.

Thus, the consular year dating was abandoned in practice, even though it formally remained until the end of the 9th century.

Thus, there remained a net total of 3. 55 million workers in as many households for whom jobs were to be provided.

Thus they remained till the Wednesday of Easter week, and Kaloyan had by that time approached so near, that he encamped at about five leagues from the Crusaders.

Thus, by the spring of 1860, only four states remained in Italy — the Austrians in Venetia, the Papal States ( now minus the Legations ), the new expanded Kingdom of Piedmont-Sardinia, and the Kingdom of the Two Sicilies.

Thus, the trade was canceled and all aforementioned players remained with their original teams.

Thus ecclesiastical intercourse between Rome and Constantinople was restored, but the mutual reserve over the dogmatic question of Monothelitism remained.

Thus the gouvernements became hollow structures, but they still carried a sense of the old provinces, and so their names and limits have remained popular until today.

Thus, a series victory in India, which Australia had not achieved since 1969 – 70, remained elusive.

Thus the county seat was established at McPherson and has remained since.

Thus, the Graham Lakes region has remained entirely rural, and the lake shores of both East Graham Lake and West Graham Lake remain undeveloped.

Thus it stresses that Edward voluntarily remained celibate, something unlikely to have been true and not corroborated by any other source.

Thus many of Repton's 400 or so designs remained wholly or partially unexecuted and, while Brown became very wealthy, Repton's income was never more than comfortable.

Thus Spoke Zarathustra remained unpopular as a topic for scholars ( especially those in the Anglo-American analytic tradition ) until the second half of the twentieth century brought widespread interest in Nietzsche and his unconventional style that does not distinguish between philosophy and literature.