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 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.

Thus each function has an infinite number of antiderivatives.

Thus, both the x and y-axes are asymptotes of the curve.

Thus, a single " rule ," like mapping every real number x to x < sup > 2 </ sup >, can lead to distinct functions and, depending on whether the images under that rule are understood to be reals or, more restrictively, non-negative reals.

In particular, one should think of the condition number as being ( very roughly ) the rate at which the solution, x, will change with respect to a change in b. Thus, if the condition number is large, even a small error in b may cause a large error in x.

Thus, the red plane shows the points with x = 1, the blue plane shows the points with z = 1, and the yellow plane shows the points with y =− 1.

Thus, the Jones vector represents ( relative ) amplitude and ( relative ) phase of electric field in x and y directions.

Thus there is a number x ≡ ( q − 1 )< sup >( p − 2 )</ sup > for which ( q − 1 )· x ≡ 1 ( mod p ), and therefore a number k for which ( q − 1 )· x − 1 = kp.

Thus 2 < sup >( q − 1 ) x </ sup >/ 2 < sup > kp </ sup >

Thus a is considered to be a parameter: it is less variable than the variable x or y, but it is not an explicit constant like the exponent 2.

Thus, substituting y with a function of x gives:

Thus, 3 + ( 6 * 4 ) is 27 which is exactly the number in a 3 x 3 x 3 larger cube.

Thus, if x

Thus, ( 1 – x ) would represent the operation of selecting all things in the world except horned things, that is, all not horned things, and ( 1 – x ) ( 1 – y ) would give all things neither horned nor sheep.

Thus each timeslot sends and receives an 8-bit PCM sample, usually encoded according to A-law algorithm, 8000 times per second ( 8 x 8000 x 32 = 2, 048, 000 ).

Thus for English the " e " box is the largest while the " j ", " k ", " q ", " x ", and " z " boxes are the smallest.

Thus, his definition of continuity required an infinitesimal change in x to correspond to an infinitesimal change in y.

Thus areas can be measured in square metres ( m < sup > 2 </ sup >), square centimetres ( cm < sup > 2 </ sup >), square millimetres ( mm < sup > 2 </ sup >), square kilometres ( km < sup > 2 </ sup >), square feet ( ft < sup > 2 </ sup >), square yards ( yd < sup > 2 </ sup >), square miles ( mi < sup > 2 </ sup >), and so forth.

Thus, if P is a program in L < sub > 2 </ sub > which is a minimal description of s, then InterpretLanguage ( P ) returns the string s. The length of this description of s is the sum of

Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c < sub > 1 </ sub >-− 3 c < sub > 1 </ sub > will cause them to be renumbered from 0 through 9 and 4 through 23, respectively.

Thus this class of molecules belong to the D < sub > 2d </ sub > point group.

Thus, few drops of diamminesilver ( I ) hydroxide ( Ag ( NH < sub > 3 </ sub >)< sub > 2 </ sub > OH ) reacts with terminal alkynes signaled by formation of a white precipitate of the silver acetylide.

Thus for an ion which traverses a 1 m flight path, across a time of 2000 ns, given an initial accelerating voltage of 5000 V and noting that one amu is 1 × 10 < sup >− 27 </ sup > kg, the mass-to-charge ratio ( more correctly the mass-to-ionisation value ratio ) becomes Z amu / charge.

Thus, oxygen is reduced to water and the original electron acceptors NAD < sup >+</ sup > and quinone are regenerated.

Thus, for example, the English form is is an apparent cognate of German ist, Latin est and Russian < nowiki > jest '</ nowiki >, even though the Germanic, Italic, and Slavic language groups split at least three thousand years ago.

Thus, the molecular formula of ethanol may be written in a paper in conformational, three-dimensional, full two-dimensional ( indicating every bond with no three-dimensional directions ), compressed two-dimensional ( CH < sub > 3 </ sub >– CH < sub > 2 </ sub >– OH ), separating the functional group from another part of the molecule ( C < sub > 2 </ sub > H < sub > 5 </ sub > OH ), or by its atomic constituents ( C < sub > 2 </ sub > H < sub > 6 </ sub > O ), according to what is discussed.

Thus ℵ < sub > 0 </ sub > is a regular cardinal.