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Thus and did
Thus a new pattern of days began to develop, for Granny Albright did not die.
Thus, theory and doctrine applicable among the great nations and the smaller European states did not really comfortably fit less developed and less powerful societies elsewhere.
Thus, while it remains possible that the Babylonians and/or the Pythagoreans may perhaps have had the magic square of three before the Chinese did, more definite evidence will have to turn up from the Middle East or the Classical World before China can lose her claim to the earliest known magic square by more than a thousand years.
Thus, the Mahayana metaphysic of mystical union for salvation was distilled down to a bare self-seeking, and for this reason, the mystic in Asia did not long remain in isolated contemplation.
Thus the limbs of the castrati often grew unusually long, as did the bones of their ribs.
Thus the court held that practices such as sleep deprivation, subjecting individual to intense noise and requiring them to stand against a wall with their limbs outstretched for extended periods of time, did not constitute torture.
Thus he supported the Irish independence movement and the anti-czarist Russian Revolution of 1917, but did not approve of Vladimir Lenin.
Thus, he had learned some Mayan, but he did not speak Nahuatl.
Thus the decision to involve the Inquisition, which therefore did not instigate the trial and in fact showed a reluctance throughout its duration.
Thus, Nathanael ’ s question, “ Can anything good come out of Nazareth ?” is consistent with a negative view of Nazareth in the canonical gospels, and with the Johannine proclamation that even his brothers did not believe in him.
Thus this type of land appropriation did not violate the Lockean proviso – there was " still enough, and as good left.
Thus, Jevons anticipated a key feature of the RSA Algorithm for public key cryptography, although he certainly did not invent the concept of public key cryptography.
Thus, Adam's sin was " to set a bad example " for his progeny, but his actions did not have the other consequences imputed to original sin.
Thus the Father did suffer and experienced all that Jesus did up to his death.
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, Stephen strengthened his power in Transdanubia, but several parts of Hungary still did not accept his rule.
Thus the kings of Epirus claimed their lineage from Achilles, and so did Alexander the Great, whose mother was of that royal house.
Thus the Augustinian theodicist would argue that the problem of evil and suffering is void because God did not create evil ; it was man who chose to deviate from the path of perfect goodness.
Thus the towpath on the Chesterfield Canal changes to the south bank while it passes through the Osberton Estate, as the Foljambes, who lived in Osberton Hall, did not want boatmen passing too close to their residence.
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 is the case judged concerning which ye did inquire.
Thus, empirical observations of the frequency of spoiled elections do not provide a good measure of how prone to spoiling the voting method is, since the observations omit the relevant information about potential candidates ( e. g., Hillary Clinton ) who did not run because they did not want to spoil the election.

Thus and function
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, if public pressure sets the effective limit to the price that the industry may charge, this pressure is itself a function of the wage rate.
Thus the negation of the axiom of choice states that there exists a set of nonempty sets which has no choice function.
Thus, the function of antioxidant systems is not to remove oxidants entirely, but instead to keep them at an optimum level.
Thus the Bauhaus style, also known as the International Style, was marked by the absence of ornamentation and by harmony between the function of an object or a building and its design.
Thus the function cannot access memory out-of-bounds.
Thus any non-constant entire function must have a singularity at the complex point at infinity, either a pole for a polynomial or an essential singularity for a transcendental entire function.
Thus, it was not until two centuries had passed that in 1872 Karl Weierstrass presented the first definition of a function with a graph that would today be considered fractal, having the non-intuitive property of being everywhere continuous but nowhere differentiable.
Thus, any periodic summation in the frequency domain can be represented by a Fourier series, whose coefficients are samples of a related continuous time function:
Thus the DTFT of the s sequence is also the Fourier transform of the modulated Dirac comb function .< ref group =" note "> We may also note that:
Thus we have the important result that when a discrete data sequence, s, is proportional to samples of an underlying continuous function, s ( t ), one can deduce something about the continuous Fourier transform, S ( ƒ ).
Thus, we would say that the function is decomposed into functions.
Thus, the gamma function must be undefined at those points ; it is a meromorphic function with simple poles at the nonpositive integers.
Thus, the hash function only hints at the record's location — it tells where one should start looking for it.
Thus, a function with a codomain is invertible if and only if it is both injective ( one-to-one ) and surjective ( onto ).
Thus, the statement that f is an idempotent unary operation on S is equivalent to the statement that f is an idempotent element with respect to the function composition operation ∘ on functions from S to S.
Thus, they capture the idea of function composition within a set.
Thus, every MUMPS command or function name could be abbreviated from one to three letters in length, e. g. Quit ( exit program ) as Q, $ P
Thus for map projections we must introduce the concept of point scale, which is a function of position, and strive to keep its variation within narrow bounds.
Thus, the logarithm function is an isomorphism from the group of positive real numbers under multiplication to the group of real numbers under addition, represented as a function:
Thus, the neurochemical alterations which induce psychosis in otherwise healthy people are indicative that the root of the symptoms altered thalamocortical and hippocamalcortical transmission, and corresponding layer 5 / thalamus axis function, altering the crucial ordered cortiocortical layer 3 / 1 and 2 / 3 transmission necessary for rational language self-expression.
Thus, modern automatic rifles overlap to an extent in design and function with machine guns.

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