Since is the distance from a given number to the mean, one way to interpret this property is as saying that the numbers to the left of the mean are balanced by the numbers to the right of the mean.

Since this holds true when performing addition on any real numbers, we say that " addition of real numbers is an associative operation.

Since its inception Beechcraft has resided in Wichita, Kansas, also the home of chief competitor Cessna, the birthplace of Learjet and of Stearman, whose trainers were used in large numbers during WW2.

Since B < sub > n </ sub >= 0 for all odd n > 1, and many formulas only involve even-index Bernoulli numbers, some authors write B < sub > n </ sub > instead of B < sub > 2n </ sub >.

Since the mass numbers of these are 12, 13 and 14 respectively, the three isotopes of carbon are known as carbon-12, carbon-13, and carbon-14, often abbreviated to < sup > 12 </ sup > C, < sup > 13 </ sup > C, and < sup > 14 </ sup > C.

Since it reflects spoken language, it does not use the positional system as in Arabic numerals, in the same way that spelling out numbers in English does not.

A set S is called countable if there exists an injective function f from S to the natural numbers Since there is an obvious bijection between and it makes no difference whether one considers 0 to be a natural number of not.

Since the NCAA has yet to recognize cheerleading as an official college sport, there are no solid numbers on college cheerleading, yet when it comes to injuries, 67 % of female athlete injuries at the college level are due to cheerleading mishaps.

Since Cartesian coordinates are unique and non-ambiguous, the points of a Cartesian plane can be identified with all possible pairs of real numbers ; that is with the Cartesian product, where is the set of all reals.

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

Since the late 1990s, Dublin has experienced a significant level of net immigration, with the greatest numbers coming from the European Union, especially the United Kingdom, Poland and Lithuania.

Since 1980, the Dead Sea basin has been dry and the algae and the bacteria have not returned in measurable numbers.

Since the larger of the two numbers is reduced, repeating this process gives successively smaller numbers until one of them is zero.

Since 1989-867 = 1122, we form a new pair of numbers

Since the two numbers are equal, we have found the answer: the greatest common divisor of 1989 and 867 must be 51.

Since every sequence of real numbers can be used to construct a real not in the sequence, the real numbers cannot be written as a sequence — that is, the real numbers are not countable.

Since real numbers can be represented as distances or intervals on a line, the slide rule was invented in the 1620s to allow multiplication and division operations to be carried out significantly faster than was previously possible.

# Large number of similar exposure units: Since insurance operates through pooling resources, the majority of insurance policies are provided for individual members of large classes, allowing insurers to benefit from the law of large numbers in which predicted losses are similar to the actual losses.

Since the left-hand side of this equation is a series of non-negative numbers, and that it converges to

Since the circulating thyroid hormones are the amino acids thyroxine and tri-iodothyronine ( cf. Section C ), it is clear that some mechanism must exist in the thyroid gland for their release from proteins before secretion.

Since n grows faster than log < sub > 2 </ sub >( n ), there must exist a value n < sub > 0 </ sub > such that

Since the Universe could, under different circumstances, conceivably not exist ( contingency ), its existence must have a cause – not merely another contingent thing, but something that exists by necessity ( something that must exist in order for anything else to exist ).

Since it is possible for such things not to exist, there must be some time at which these things did not in fact exist.

Since then Mao's peasant revolutionary vision and so-called " continued revolution under the dictatorship of the proletariat " stipulated that class enemies continued to exist even though the socialist revolution seemed to be complete, giving way to the Cultural Revolution.

Since thousands of different types of wood products manufacturing plants exist around the globe, and may be integrated ( lumber, plywood, paper, etc.

Since then many clubs have admitted women, but some all-male clubs still exist.

Since organic compounds often exist as mixtures, a variety of techniques have also been developed to assess purity, especially important being chromatography techniques such as HPLC and gas chromatography.

Since evil has no positive reality of its own, it cannot be caused to exist, and so God cannot be held responsible for causing it to exist.

Since primitive worlds exist near technological worlds, primitive weapons are also typically included, such as swords, shields, pikes, bows, and so on.

Since most physicists would consider the statement of the underlying rules to suffice as the definition of a " theory of everything ", most physicists argue that Gödel's Theorem does not mean that a ToE cannot exist.

Since the late 1950s, aerospace engineers have used the term " unobtainium " when referring to unusual or costly materials, or when theoretically considering a material perfect for their needs in all respects, except that it does not exist.

Since none have been proven to exist already then the drive is impossible to construct, even if the metric is physically meaningful.

Since adjoint functors exist in abundance, this gives numerous examples of continuous and cocontinuous functors.

Since they exist, we cannot simply ignore them, for once we include the interaction between the electron and the electromagnetic field, any electron placed in a positive-energy eigenstate would decay into negative-energy eigenstates of successively lower energy by emitting excess energy in the form of photons.

Since a clear archetype for determining guilt does not exist, the criminal justice system must rely on rulings handed down by juries.

Since the supremum and infimum of an unbounded set of real numbers may not exist ( the reals are not a complete lattice ), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the complete totally ordered set, which is a complete lattice.

Since the shields are not perfect conductors, electric fields can exist inside the shield, thus allowing radiating electromagnetic fields to go through the shield.

Since physics needs to talk about numbers in offering any of its explanations, then numbers must exist.

Since the meaning of the existential quantifier in formal notation is usually explained in terms of its equivalence to English expressions such as " there is " and " there exist ", and since these English expressions are not reliably ontologically committing, it comes to seem that we cannot be sure of our theory's ontological commitments even after it has been regimented into a canonical formulation.

Since but-for causation is very easy to show and does not assign culpability ( but for the rain, you would not have crashed your carthe rain is not morally or legally culpable but still constitutes a cause ), there is a second test used to determine if an action is close enough to a harm in a " chain of events " to be a legally culpable cause of the harm.

Since the requirements of devices such as computers, printers, test instruments, POS terminals and so on were not considered by the standard, designers implementing an RS-232 compatible interface on their equipment often interpreted the requirements idiosyncratically.

Since Brown and Lenneberg believed that the objective reality denoted by language was the same for speakers of all languages, they decided to test how different languages codified the same message differently and whether differences in codification could be proven to affect behavior.

Since the reinforced carbon-carbon ( RCC ) panel on Columbia had only 40 % of the strength of the test panel from Enterprise, this result suggested that the RCC leading edge would have been shattered.

Since the introduction of MRI this test is rarely necessary to diagnose syringomyelia.

Since the Ottoman Empire never attacked again, the fortifications were never put to the test, and today remain one of the best-preserved fortifications of this period.

Since individual harmonic amplitudes are measured, it is required that the manufacturer disclose the test signal frequency range, level and gain conditions, and number of measurements taken.

Since the Amiga's hardware was more or less fixed ( unlike today's PC industry, where arbitrary combinations of hardware can be put together ), there was competition to test the limits of that hardware and perform theoretically " impossible " feats by refactoring the problem at hand.

Since its inception, the newly created Department of Homeland Security has conducted at least three exercises to test continuity plans.

Since the calorimeter runs in an adiabatic environment, any heat generated by the material sample under test causes the sample to increase in temperature, thus fuelling the reaction.

Since a jury is intended to be an impartial panel capable of reaching a verdict, there are often procedures and requirements, for instance, fluent understanding of the language, or the ability to test jurors or otherwise exclude jurors who might be perceived as less than neutral or more partial to hear one side or the other.

Since the gain has been measured with respect to this reference antenna, the difference in the gain of the test antenna is often compared to that of the dipole.

Since then PETRA serves HASYLAB as a source of high-energy synchrotron radiation and for this purpose possesses three test experimental areas.

Since then, Detachment 2 has partnered with the warfighter and the developmental test community to provide the most thorough and rigorous operational test programs found anywhere in the world.

( Since people seldom sincerely declare to a prospective employers their past deviance, the " integrity " testers adopted an indirect approach: letting the work-candidates talk about what they think of the deviance of other people, considered in general, as a written answer demanded by the questions of the " integrity test ".

Since the test for polysemy is the vague concept of relatedness, judgments of polysemy can be difficult to make.

Since the WEKAF system is more risky, it is preferred by many practitioners who want to test themselves.

Since then, the three-step test has been modified and transplanted into the Agreement on Trade-Related Aspects of Intellectual Property Rights, the WIPO Copyright Treaty ( Article 10 ), the WIPO Performances and Phonograms Treaty, the Directive on the legal protection of computer programs ( Article 6 ( 3 )), the EU Database Directive ( Article 6 ( 3 )), and the EU Copyright Directive ( Article 5 ( 5 )).

Since then, this hypothesis has been tested using the McDonald-Kreitman test, and has not been supported in all species.

Since a molecular genetic test for the ridge gene does not exist, heterozygotes are detected by mating the animal in question to either known heterozygotes or known homozygous recessives ( other methods exist such as mating to offspring, but result in inbred offspring ) and a heterozygote is detected when a ridgeless pup is born.

Since Joseph and Benjamin were born from Rachel, this test was necessary to reveal if they would betray Benjamin as they did with Joseph when he was seventeen.

Since 1994, the branch's remaining platform at Holborn ( Platform 5 ) has been used to test mock-up designs for new platform signage and advertising systems.

Since the introduction of automated analyzers into the clinical laboratory, the ESR test has been automatically performed.