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 the films seen as they came in ( coordinated for the regular sections ), were often out of context.

Thus twenty `` black souls '' were to remain ignorant of their imminent journey to the land of free men.

Thus such great American documentaries as The River and The Plow That Broke The Plains were composed as visual stories rather than as illustrated lectures.

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 #, $ and % were placed to correspond to 3, 4, and 5 in the adjacent column.

Thus the only member churches of the present Anglican Communion existing by the mid-18th century were the Church of England, its closely linked sister church, the Church of Ireland ( which also separated from Roman Catholicism under Henry VIII ) and the Scottish Episcopal Church which for parts of the 17th and 18th centuries was partially underground ( it was suspected of Jacobite sympathies ).

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

Thus Myspace and YouTube were not liable for a dyslexic man's inability to navigate the site regardless of how impressive the " online theater " is.

Thus we were spared the affliction of his absence and the triumph of suffering for his principles.

Thus we have the story of his riding across a stick ( horse made of stick ) with his children and upon being discovered by a friend desiring that he not mention till he himself were the father of children ; and because of the affection of his son Archidamus ' for Cleonymus, he saved Sphodrias, Cleonymus ' father, from execution for his incursion into the Piraeus, and dishonorable retreat, in 378 BC.

Thus for example two separate quotes by Athenaeus were united by Theodor Bergk to form fr. 362.

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.

Thus while Persian-speakers were concentrated on the lower rungs of the work force, managers tended to be brought in from some distance.

Thus, on January 16, 1997, the Diamondbacks were officially voted into the National League while their expansion counterparts in Tampa Bay were voted into the American League.

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, many users of a given BBS usually lived in the same area, and activities such as BBS Meets or Get Togethers were common, where users of the board would gather at a local restaurant, the SysOp ’ s home or similar venue and meet face to face.

Thus the discovery report by the Berkeley group reads: " It is suggested that element 97 be given the name berkelium ( symbol Bk ) after the city of Berkeley in a manner similar to that used in naming its chemical homologue terbium ( atomic number 65 ) whose name was derived from the town of Ytterby, Sweden, where the rare earth minerals were first found.

" Thus the farmers were placed in a disadvantageous economic position.

Thus, dark blue jerseys, were introduced with white shorts and the red socks of 1908.

Thus, if the score was 3 – 2 with the bases loaded in the bottom of the ninth, and the batter smacked an " over the fence home run ", the game would end at 4 – 3, with the batter only allowed a double, and the runners officially stopped on 2nd and 3rd ( since they were not needed to win the game ).

Thus in 1880 and 1882, Benedictine teaching monks were effectively exiled ; this was not completed until 1901.

Thus, in 250-1, the Bastarnae were probably involved in the Gothic and Sarmatian invasions which culminated in the Roman defeat at the Battle of Abrittus and the slaying of the emperor Decius ( 251 ).

Thus parliamentary constituencies were derived from the ancient boroughs.

Thus, intuitionists are ready to accept a statement of the form " P or Q " as true only if we can prove P or if we can prove Q:

Thus, the goal of a conditional proof is to demonstrate that if the CPA were true, then the desired conclusion necessarily follows.

Thus, though knowledge requires justification, truth, and belief, the word " knowledge " can't be, according to Williamson's theory, accurately regarded as simply shorthand for " justified true belief.

Thus a statement of the form is said to be true, under a particular interpretation, if there is some object in the domain of discourse of that interpretation that satisfies the predicate that the interpretation uses to assign meaning to the symbol Phil.

Thus the songs of Uttarakhand are a true reflection of the Cultural Heritage and the way people live their lives in the Himalayas.

Thus for iconoclasts the only true ( and permitted ) " icon " of Jesus was the Eucharist, which was believed to be his body and blood.

Thus Irenaeus provides the earliest witness to the assertion of the four canonical Gospels, possibly in reaction to Marcion's edited version of the Gospel of Luke, which Marcion asserted was the one and only true gospel.

Thus ( D1 ) is both true and false.

Thus, for example, the statement, " It is true that two plus two equals four ", contains no more information than the statement " two plus two equals four ", because the phrase " it is true that ..." is always implicitly there.

Thus for a theory " T ", " G " is true, but not provable in " T ".

Thus, in the cases listed above, the disjunction of and is true in all cases except 4.

Thus it is true in every case above except case 2, because this is the only case when is true but is not.

Thus to Brouwer, we are not justified in asserting " either Goldbach's conjecture is true, or it is not.

Thus, the statement " there are no contradictions in the Principia system " cannot be proven in the Principia system unless there are contradictions in the system ( in which case it can be proven both true and false ).

Thus, according to the law of non-contradiction, " not p " must be false, and so, according to the law of the excluded middle, p is true.

Thus, many scholars will call a body of stories " mythology ", leaving open the question of whether the stories are true or false.

Thus, a difference in true wind creates a different apparent wind at different heights.

" Thus without holding a proposition up against the real world, we cannot tell whether the proposition is true or false.

Thus in Puget Sound itself, the names given by Wilkes are common and Spanish names rare, while the reverse is true for the San Juan and Gulf Islands ( although the Spanish did not explore Puget Sound as thoroughly as the British and Americans, resulting in fewer Spanish names to start with ).

Thus the Council Fathers meant to say that the being of the Church as such is a broader entity than the Roman Catholic Church, but within the latter it acquires, in an incomparable way, the character of a true and proper subject.

Thus, there is no such thing as a sentence, term, expression or word symbolically representing a single true meaning ; it is underspecified ( which cat sat on which mat?

Thus this report of a feud between Eadwig and Dunstan could either have been based on a true incident of a political quarrel for power between a young king and powerful church officials who wished to control the king and who later spread this legend to blacken his reputation, or it could be an urban legend ; the Chronicle also tells of Odo putting aside the King's marriage on the grounds Eadwig and his wife were " too related ".

Thus, the subaltern relationship between universal and existential also does not hold, since for a nonexistent S, " All S is P " is true but does not entail " Some S is P ", which is false.