Since computers can make arithmetic calculations much faster and more accurately than humans, it was thought to be only a short matter of time before the technical details could be taken care of that would allow them the same remarkable capacity to process language.

Since the hour number starts over after it reaches 12, this is arithmetic modulo 12.

Since the axioms in the schema in ( 5 ) cannot be replaced by any finite number of axioms, Presburger arithmetic is not finitely axiomatizable.

Since the simple arithmetic operators are all binary ( at least, in arithmetic contexts ), any prefix representation thereof is unambiguous, and bracketing the prefix expression is unnecessary.

Since that time, patents on various well-known arithmetic coding techniques have also expired.

Since any such axiom system would contain the finitary arithmetic as a subsystem, Gödel's theorem implied that it would be impossible to prove the system's consistency relative to that ( since it would then prove its own consistency, which Gödel had shown was impossible ).

Since the earliest days of computer architecture, some CPUs have added several additional arithmetic logic units ( ALUs ) to run in parallel.

Since the fundamental theorem of arithmetic applied to a non-zero integer n that is neither 1 nor − 1 also asserts uniqueness of the representation for p < sub > i </ sub > prime and e < sub > i </ sub > positive, a primary decomposition of ( n ) is essentially unique.

Since there are two elements in this remaining list, the median is their arithmetic mean, ( 3 + 7 )/ 2

Since then, floating-point arithmetic and " arbitrary-precision " modes have been added, the latter of which emulates an arbitrarily large mantissa in RAM.

Since early times, Chinese understood basic arithmetic ( which dominated far eastern history ), algebra, equations, and negative numbers with counting rods.

Since an arithmetic operation may produce a result larger than the maximum representable value, a potential error condition may result.

Since universal codes are simpler and faster to encode and decode than Huffman codes ( which is, in turn, simpler and faster than arithmetic encoding ), the universal code would be preferable in cases where D < sub > KL </ sub >( q || p ) is sufficiently small.

Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds.

Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become a particularly active area in group theory.

Since surface area is a geometric notion, areas of congruent surfaces must be the same and area must depend only on the shape of the surface, but not on its position and orientation in space.

Since matrix schemes follow the same laws of geometric progression as pyramids, they are subsequently as doomed to collapse.

Since the geometric line of sight passes at varying heights over the Earth, the propagating radio wave encounters slightly different propagation conditions over the path.

Since the techniques of calculus were unknown, it was generally presumed that a squaring should be done via geometric constructions, that is, by compass and straightedge.

Since Michel Chasles cited this book of Pappus in his history of geometric methods, it has become the object of considerable attention.

Since any eigenvector is also a generalized eigenvector, the geometric multiplicity is less than or equal to the algebraic multiplicity.

Since upper and lower bounds of the true cost of living index can be found, respectively, through the Laspeyres and Paasche indices, the geometric average of the two, known as the Fisher price index, is a close approximation of the true cost of living index if the upper and lower bounds are not too far apart.

Since the lattices of flats of matroids are exactly the geometric lattices, this implies that the lattice of partitions is also geometric.

Since the exterior derivative is a natural operator, in a sense that can be given a technical meaning, such equations are intrinsic and geometric.

Since a conductor is a flexible object with uniform weight per unit length, the geometric shape of a conductor strung on towers approximates that of a catenary.

Since a relativistic transformation rotates space and time into each other much as geometric rotations in the plane rotate the x and y axes, it is convenient to use the same units for space and time, otherwise there is a unit conversion factor which converts incessantly between the units.

Since alkene geometric isomers are also classified as diastereomers, this reaction would also be called diastereoselective.

Since the 1995 book Fluid Concepts and Creative Analogies describing the work of the Fluid Analogies Research Group ( FARG ) book, work on Copycat-like models has continued: as of 2008 the latest models are Phaeaco ( a Bongard problem solver ), SeqSee ( number sequence extrapolation ), George ( geometric exploration ), and Musicat ( a melodic expectation model ).

Since God created the universe after geometric and harmonic principles, to seek these principles was therefore to seek and worship God.

Since then, dissection puzzles have been used for entertainment and maths education, and creation of complex dissection puzzles is considered an exercise of geometric principles by mathematicians and math students.

Since it is the purpose of the U. S. numbered system to mark the best and shortest route available, an alternate route should be designated only where both routes are needed to accommodate the traffic demand, and when the alternate route has substantially the same geometric and structural design standards of the main marked routing.

Since the Catholic Church expresses such desire that the Sacred Scriptures be read, the following taken from the Holy Bible ( New Catholic Edition ) will prove a means of grace and a source of great spiritual blessing.

Since p ( x ) is irreducible, this means that p ( x ) = k ( x − a ), for some k ∈ F

Since one person needs to cover the entire court, singles tactics are based on forcing the opponent to move as much as possible ; this means that singles strokes are normally directed to the corners of the court.

Since a leg theory attack means the batsman is more likely to hit the ball on the leg side, additional fielders on that side of the field can be effective in preventing runs and taking catches.

Since the early 20th century it has been commonly accepted that Old Irish Bel ( l ) taine is derived from a Common Celtic * belo-te ( p ) niâ, meaning " bright fire " ( where the element * belo-might be cognate with the English word bale in ' bale-fire ' meaning ' white ' or ' shining '; compare Anglo-Saxon bael, and Lithuanian / Latvian baltas / balts, found in the name of the Baltic ; in Slavic languages byelo or beloye also means ' white ', as in Беларусь ( White Russia or Belarus ) or Бе ́ лое мо ́ ре Sea ).

Since there are infinitely many positive integers, this means that there are positive integers that cannot be defined by phrases of under eleven words.

Since most Western economies are now considered " open " with free capital movement, this essentially means that central banks may target interest rates or exchange rates with credibility, but not both at once.

Since the complex numbers can be multiplied giving another complex number, this identification provides a means to " multiply " vectors.

Since Fjorgyn is not only the name of a goddess, but the feminine byname for Earth, it is relatively safe to assume that " mær ", in this case, means " daughter ".

Since the early days of writing politicians, diplomats and military commanders understood that it was necessary to provide some mechanism to protect the confidentiality of correspondence and to have some means of detecting tampering.

Since the Human Rights Act 1998 came into force, in those cases alone, the inquest is now to consider the broader question " by what means and in what circumstances ".

Since this is what ( B ) itself states, it means that ( B ) must be true.

Since the names of functions are largely a convenience, the lambda calculus has no means of naming a function.

Since 2001, trim levels are also indicated by including a number after the main index: '- 00 ' means base trim level, '- 01 ' means standard trim and '- 02 ' designates deluxe version ; for example, VAZ-21121-02 means Lada 112 hatchback with an 1. 6L SOHC engine and deluxe trim.

Since all services are performed by usermode programs, efficient means of communication between programs are essential, far more so than in monolithic kernels.

Since the launch of the third generation MX-5, Mazda consolidated worldwide marketing using the MX-5 name, though enthusiasts in the US still refer to it as Miata, a name that means " reward " in Old High German, and the vehicle in 2012 was still marketed by Mazda in the US as the MX-5 Miata.

Since the Temple was an enclosed place with no natural light, some means of illumination must have existed.

Since reason is the means of human knowledge, it is therefore each person's most fundamental means of survival and is necessary to the achievement of values.

Since the overall annual passive quota for the United States is 42, this means that it will be obligated to accept no more than 31 observation flights a year during this three-year period.

Since G is the midpoint of line FQ, this means that

If one adds two whole parts the result is one whole and if one whole is subtracted from another whole the result is another whole-it means there is one whole universe and it is all prevaded by " Him ". Since the universe has come forth from the Divine, all things and beings are sacred and must be treated so in human thought and action.

* Since the skull ossifies over the brain during infant development, external craniological means could be used to diagnose the internal states of the mental characters