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

Since various Molly Pitcher tales grew in the telling, many historians regard Molly Pitcher as folklore rather than history, or suggest that Molly Pitcher may be a composite image inspired by the actions of a number of real women.

* Since Big Brother 2, the UK series always opens with a twist which have included the public being able to choose the final housemate out of three possibilities ( Big Brother 2 ), the public voting for a housemate to leave during the first week and then the housemates choosing between the two housemates with the least number of votes ( Big Brother 3 ), First Night Nominations ( Big Brother 4 ), Suitcase Nominations ( Big Brother 5 ), Unlucky Housemate 13 ( Big Brother 6 ), Big Brother Hood ( Big Brother 7 ), an all-female House and the first inclusion of twins as contestants ( Big Brother 8 ), the first couple to enter as housemates and set a secret task to hide their real relationship ( Big Brother 9 ), all " housemates " really being " non-housemates " who had to earn their housemate status ( Big Brother 10 ), a mole entering the House with an " Impossible Task " ( Big Brother 11 ), Jackie Stallone entering a house containing her son's ex-wife ( Celebrity Big Brother 3 ), the entrance of a non-celebrity in a celebrity edition ( Celebrity Big Brother 4 ) and Jade Goody's family announced to be visiting.

Since then, real estate development in the area has continued robustly.

Since inflation lowers real wages, Keynesians view inflation as the solution to involuntary unemployment.

Since tangents and inverse tangents are both continuous, our identification function is a homeomorphism between the real line and the unit circle without ∞.

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 underlying behaviour doesn't violate local causality, it follows that neither does the additional effect of wavefunction collapse, whether real or apparent.

Since 1968, however, the lowest published count for power-of-two was long achieved by the split-radix FFT algorithm, which requires real multiplications and additions for.

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 political power belongs to the sole legal party, in certain states under Marxist constitutions of the constitutionally socialist state type inspired by the former Union of Soviet Socialist Republics ( USSR ) and its constitutive Soviet republics, there was no formal office of head of state, but rather the leader of the legislative branch was considered to be the closest common equivalent of a head of state as a natural person.

Since " Barbellion " was the real author's pen name, many reviewers believed Wells to have been the true author of the Journal ; Wells always denied this, despite being full of praise for the diaries, but the rumours persisted until Barbellion's death later that year.

Since then, " Sang real " is sometimes employed to lend a medievalising air in referring to the Holy Grail.

Since nothing other than an intelligent cause has been demonstrated to be able to yield such a strong appearance of design, Darwinian claims notwithstanding, the conclusion that the design seen in life is real design is rationally justified.

Since that time, the parliament has demonstrated real independence from the executive branch.

Since that time, Parliament has demonstrated real independence from the executive branch.

Since the early 1980s, the Moroccan government has pursued an economic program toward accelerating real economy growth with the support of the International Monetary Fund, the World Bank, and the Paris Club of creditors.

Since the two teams play each other so infrequently in the regular season, some, including players on both teams, have questioned whether the Giants and Jets have a real rivalry.

Since the city authorities would not allow the new line to breach the customs wall, still standing at the time, it had to stop just short, at Potsdamer Platz, but it was this that kick-started the real transformation of the area, into the bustling focal point that Potsdamer Platz would eventually become.

Since an actual tract of land could not literally be brought into a courtroom as a person could, this was effected by giving notice upon the real property itself.

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

Since Carmichael numbers exist, this primality test cannot be relied upon to prove the primality of a number, although it can still be used to prove a number is composite.

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.

# 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 hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Since we can neither undo nor redo the past, we are limited to the events of today and tomorrow.

Since broadcast frequencies are very limited in number, these objectives are to some extent inconsistent in that not all of them can be fully realized, and to the extent that each is realized, there is a corresponding reduction of the possibilities for fullest achievement of the others.

Since he can neither accept nor reject them all, he must be governed by the time and energy available for his prime professional obligations.

Since a Skeletal Age rating can be made at any age during growth, from Elbow, Shoulder, Knee, or Foot as well as Hand, it seems to be the method of choice when one wishes to study most aspects of skeletal developmental progress during childhood.

A final class of exceptional lines is identifiable from the following considerations: Since no two generators of Af can intersect, it follows that their image curves can have no free intersections.

Since morale is closely related to pattern maintenance and integration, the higher the morale and solidarity, the better the system can solve the problems of the system.

Since the writer had not noticed this characteristic in married students scattered throughout the various sections previous to this experiment, nor, as a matter of fact, in those who were continuing in `` single sections '', he can only conclude that there must have been something `` contagious '' within the specific group which caused this to occur.

Since effective area coverage appears fairly remote, the requirement can be borne in mind while considering the elements: air, surface, sub-surface, fixed installations, mines, and intelligence.

Since the load L, under actual cutting conditions is caused by Af, it can be seen that Af

Since we are considering here relatively small diameter ( 1 - 1.5 inches ) fiber plates, their average thickness can be kept below 1/4 inch and their internal losses may be assumed as 15 percent ( per plate ).

Since the change to better nutrition, he feels he can report on improvements in health, though he considers the following statements observations and not scientific proof.

Since rococo music tends to be pretty and elegant above all, it can seem rather vacuous to twentieth-century ears that have grown accustomed to the stress and dissonances of composers from Beethoven to Boulez.

`` Since we're having coffee with them this afternoon '', he said, `` I think I'll ask the daughter if we can pay her to come in every day to clean for us ''.

Since altruism takes away resources from the altruist it can be a " honest signal " of resource availability and the abilities needed to gather resources.

Since the minting of coins was a prerogative accorded in Islamic practice only to a sovereign, it can be considered that Osmanli became independent of the Mongol Khans.

Since in oral languages the elements of sound are for the most part produced linearly in time ( that is, in a word like cat the a sound comes after the c sound, and the t sound comes after that ), they can generally be easily written in a linear ( one-dimensional ) writing system such as an alphabet.

Since Java's bytecode is platform-independent, Java applets can be executed by browsers running under many platforms, including Windows, Unix, Mac OS, and Linux.

Since the fluctuations are assumed to be small, products of the fluctuation terms can be neglected ( to first order ) and we have

Since all anchors that embed themselves in the bottom require the strain to be along the seabed, anchors can be broken out of the bottom by shortening the rode until the vessel is directly above the anchor ( at this point the anchor chain is " up and down " in naval parlance ).

Since 4 % can be expressed as. 04, gives the amount of alcohol in terms of ml — which, when divided by, shows the number of units.

Since algorithms are platform-independent ( i. e. a given algorithm can be implemented in an arbitrary programming language on an arbitrary computer running an arbitrary operating system ), there are significant drawbacks to using an empirical approach to gauge the comparative performance of a given set of algorithms.

Since the target audience of pop music can vary greatly, so can the celebrated subject of the anthem.