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 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 an 8-course Renaissance lute will usually have 15 strings, and a 13-course Baroque lute will have 24.

Thus, the vocal lines for Papageno — sung by Schikaneder himself — and Monostatos ( Johann Joseph Nouseul ) are often stated first in the strings so the singer can find his pitch, and are frequently doubled by instruments.

Thus one prevents long strings without change via such devices as run length limited codes.

Thus the full dictionary does not need be sent with the encoded data ; just the initial dictionary containing the single-character strings is sufficient ( and is typically defined beforehand within the encoder and decoder rather than being explicitly sent with the encoded data.

Thus, the performer plays on two strings most of the time, creating a typical bourdon style.

Thus, the tuning hammer is used on the top side of the wrest plank, but the strings are wrapped around the pins on the bottom side.

Thus, it needs to be capoed individually since it is not covered by a capo on the other four strings.

Thus the strings are about 25 cm above the floor.

Thus, when used to aid in fuzzy string searching in applications such as record linkage, the compared strings are usually short to help improve speed of comparisons.

Thus, if two strings have the same digest, one can be very confident that they are identical.

Thus strings, harpsichords and recorders represent the pastoral fields of Thrace with their nymphs and shepherds ; heavy brass illustrates the underworld and its denizens.

Thus, he refused to play any music for the villagers, instead hitting his lyre's strings with a rock over and over.

Thus finding more repeated strings narrows down the possible lengths of the keyword, since we can take the greatest common divisor of all the distances.

Thus, a process calculus is to a history monoid what a formal language is to a free monoid ( a formal language is a subset of the set of all possible finite-length strings of an alphabet generated by the Kleene star ).

*" Thus strings of unconnected words, and constant repetitions of words and phrases, are very properly condemned in written speeches: but not in spoken speeches — speakers use them freely, for they have a dramatic effect.

Thus, two strings in C are added by adding the bits in the strings modulo 2 ( that is, addition without carry, or exclusive disjunction ).

Thus, given actions and attributes, the grammar can be used for translating strings from its language by applying the actions and carrying information through each symbol's attribute.

If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).

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, for example, the CGS unit of pressure, barye, is related to the CGS base units of length, mass, and time in the same way as the SI unit of pressure, pascal, is related to the SI base units of length, mass, and time:

Thus, these nerve cells have a length of nearly in the largest giraffes.

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, the 1960 SI definition abandoned any explicit relationship between the scientific second and the length of a day, as most people understand the term.

Thus the area of S < sub > D </ sub > is obtained by integrating the length of the normal vector to the surface over the appropriate region D in the parametric uv plane.

Thus the length of the edges is one third of that of the original edges.

Thus, the coordinates differences ( Δx, Δy, Δz ) and ( Δξ, Δη, Δζ ) are not intrinsic to the rod, but merely reflect the reference frame used to describe it ; by contrast, the length L is an intrinsic property of the rod.

Thus the bound vector represented by ( 1, 0, 0 ) is a vector of unit length pointing from the origin along the positive x-axis.

Thus there were no waves / modes with a wavelength larger than twice the length ( L ) of the cavity.

Thus an aerial with a length corresponding to the eighth of the radiated wavelength can be extended only to a quarter-wave radiator, but not to a half wave radiator.

Thus, if a wave is traveling through several different media, then the optical path length of each medium can be added to find the total optical path length.

This question has two fundamental physical units: time t and length, and three dimensional variables: distance D, time taken T, and velocity V. Thus there is 3 − 2 = 1 dimensionless quantity.

There are 3 fundamental physical units in this equation: time t, mass m, and length l, and 4 dimensional variables, T, M, L, and g. Thus we need only 4 − 3 = 1 dimensionless parameter, denoted π, and the model can be re-expressed as

Thus, intuitively we could interpret the fraction of as representing the ratio of the labor one has to perform when going from a randomly chosen configuration to another randomly chosen configuration, relative to the difficulty of having to cross the " most difficult " path of length which involves moving all the disks from one peg to another.

Thus, if V < sub > g </ sup > is the group velocity of a phonon wave packet, then the relaxation length is defined as:

Thus, all three series are set in the same universe, giving them a combined length of 15 novels, and a total of about 1, 500, 000 words.

Thus the long and exciting discussion touching the removal of Williams College and the location of a college in some more central town of old Hampshire County at length came to an end, and the contending parties now directed all their energies to building up the institutions of their choice.

Thus, for a fixed path length, UV / Vis spectroscopy can be used to determine the concentration of the absorber in a solution.