While services in the Temple in Jerusalem included musical instruments ( 2 Chronicles 29: 25 – 27 ), traditional Jewish religious services in the Synagogue, both before and after the destruction of the Temple, did not include musical instruments given the practice of scriptural cantillation.

In this case, is the smallest σ-algebra that contains the open intervals of R. While there are many Borel measures μ, the choice of Borel measure which assigns for every interval is sometimes called " the " Borel measure on R. In practice, even " the " Borel measure is not the most useful measure defined on the σ-algebra of Borel sets ; indeed, the Lebesgue measure is an extension of " the " Borel measure which possesses the crucial property that it is a complete measure ( unlike the Borel measure ).

While animal sacrifice was part of the practice of ancient Judaism, the Tanakh ( Old Testament ) and Jewish teaching portray human sacrifice as one of the evils that separated the pagans of Canaan from the Hebrews (, ).

While capital adequacy is important, it is defined and regulated by the Bank for International Settlements, and central banks in practice generally do not apply stricter rules.

While most cartoonist decided to follow the tide, some cartoonists have complained about this, with Pogo ending in 1975 as a form of protest from its creators against the practice.

While married to Mao, Chiang adopted two concubines ( concubinage was still a common practice for well-to-do, non-Christian males in China ): he married Yao Yecheng ( 姚冶誠, 1889 – 1972 ) in 1912 and Chen Jieru ( 陳潔如, 1906 – 1971 ) in December 1921.

While on active duty, he received two lessons from Arnold Schoenberg at UCLA in an attempt to connect with High Modernism theory and practice.

While TT is strictly uniform ( being based on the SI second, every second is the same as every other second ), it is in practice realised by International Atomic Time ( TAI ) with an accuracy of about 1: 10 < small >< sup > 14 </ sup ></ small >.

Prof. Spiegelberg writes, " While outward religious practice never entered his life any more than it did that of most academic scholars of the time, his mind remained open for the religious phenomenon as for any other genuine experience.

While a slight bow to the overall developer community to allow something looking like direct access ( e. g. thereby breaking the Information Hiding Principle ), the practice is dangerous as it hides or obfuscates the reality of a " setter " being used.

While critics point to the common practice of pseudonymous writing in the ancient world, they usually fail to point out that this practice, though common in the culture, was not common in personal letters, and was categorically rejected by the early church ( cf.

While at the basic levels, meditation is geared toward relaxation, the practice of advanced meditators may be aimed toward the purpose of dividing one from their awareness of " self ," to a certain degree, and for a certain time.

While far from a cure, operant-based biofeedback based on conditioning of EEG waves has some experimental support ( see Professional practice of behavior analysis ).

While in theory King Louis XVI was an absolute monarch, in practice he was often indecisive and known to back down when faced with strong opposition.

While most of his proposals-" to abandon the gold standard, let international exchange rates float, use federal surpluses and deficits as macroeconomic policy tools that could counter cyclical trends, and establish bureaus of economic statistics ( including a consumer price index ) in order to facilitate this effort "-are now conventional practice, his critique of fractional-reserve banking still " remains outside the bounds of conventional wisdom ".

While this new career took him away from the practice of law, it was rewarding in other ways: the fees were said to yield up to $ 40, 000 ( US $ in present terms ) over the two-year term.

While she continued to practice her singing, she worked many non-singing jobs in the years after high school, including a job at Bamberger's department store.

While slopes along channels of 1: 100 have been recommended, in practice it is difficult to build a base for channels that is sufficiently true to enable nutrient films to flow without ponding in locally depressed areas.

While these were mostly intended as practice instruments for organists, a few pieces are believed to have been written specifically for the pedal harpsichord.

While he maintains his practice of the Jesus Prayer, which becomes automatic and continues twenty-four hours a day, seven days a week, the Hesychast cultivates watchful attention ( Gr. nepsis ).

While from a Catholic viewpoint there have been tensions concerning some developments of the practice, the Pope said, there is no denying the goodness of the intention that inspired its defence, which was to stress that man is offered the concrete possibility of uniting himself in his inner heart with God in that profound union of grace known as theosis, divinization.

While attempts to implement a similar system had been made before and other networks have since developed registration services of their own, at the time DALnet's successful decision to allow and enforce nickname and channel registration was considered to be unique and even controversial, as it went against established practice.

While in theory insurers could encourage investment in loss reduction, some commentators have argued that in practice insurers had historically not aggressively pursued loss control measures-particularly to prevent disaster losses such as hurricanes-because of concerns over rate reductions and legal battles.

While it is commonplace to detect their influences in Kent ( for example, the practice of partible inheritance known as gavelkind ), the Jutes in Hampshire and the Isle of Wight vanished, probably assimilated to the surrounding Saxons, leaving only the slightest of traces.

While the roots of formalised logic go back to Aristotele, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics.

While extending the notion of number by means of his revolutionary concept of infinite cardinality, Cantor was paradoxically opposed to theories of infinitesimals of his contemporaries Otto Stolz and Paul du Bois-Reymond, describing them as both " an abomination " and " a cholera bacillus of mathematics ".

While the mathematics permits calculation of many quantities that can be measured experimentally, there is a definite theoretical limit to values that can be simultaneously measured.

While Babylonian number theory — or what survives of Babylonian mathematics that can be called thus — consists of this single, striking fragment, Babylonian algebra ( in the secondary-school sense of " algebra ") was exceptionally well developed.

While Greek astronomy — thanks to Alexander's conquests — probably influenced Indian learning, to the point of introducing trigonometry, it seems to be the case that Indian mathematics is otherwise an indigenous tradition ; in particular, there is no evidence that Euclid's Elements reached India before the 18th century.

While OBE implementations often incorporate a host of many progressive pedagogical models and ideas, such as reform mathematics, block scheduling, project-based learning and whole language reading, OBE in itself does not specify or require any particular style of teaching or learning.

While working as an ambulance driver Wilson attended New York University, studying engineering and mathematics.

While in mathematics all function applications are referentially transparent, in programming this is not always the case.

While the school specialized in the humanities, Banach and his best friend Witold Wiłkosz ( also a future mathematician ) spent most of their time working on mathematics problems during breaks and after school.

While studying mathematics as an undergraduate student at Harvard College, he began to write comic songs to entertain his friends, including " Fight Fiercely, Harvard " ( 1945 ).

While mathematics can be used to calculate where and when the moving Achilles will overtake the Tortoise of Zeno's paradox, philosophers such as Brown and Moorcroft

While PM avoided the known paradoxes and allows the derivation of a great deal of mathematics, its system gave rise to new problems.

While variables in mathematics usually take numerical values, in fuzzy logic applications, the non-numeric linguistic variables are often used to facilitate the expression of rules and facts.

While Euclidean geometry, named after the Greek mathematician Euclid, includes some of the oldest known mathematics, non-Euclidean geometries were not widely accepted as legitimate until the 19th century.

While his original writings demonstrate that he had a sincere passion for the seven liberal arts ( grammar, rhetoric, logic, mathematics, geometry, music, and astronomy ), his work in Quaestiones naturales illustrated a more encompassing dedication to subjects such as physics, the natural sciences, and possibly even metaphysics.

While it is often assumed that those with this intelligence naturally excel in mathematics, chess, computer programming and other logical or numerical activities, a more accurate definition places less emphasis on traditional mathematical ability and more on reasoning capabilities, recognizing abstract patterns, scientific thinking and investigation and the ability to perform complex calculations.

While some constructs, such as mathematics, are considered to be very reliable, all human constructs are subject to humanity's assumptions of cause and effect.

While this remains the case, the " string " must be thought of either as real but untestable, or simply as an illusion or artifact of either mathematics or cognition.

While the priests taught him mathematics and Latin, his mother completed his education.

While the Mizar proof checker remains proprietary, the Mizar Mathematical Library – the sizable body of formalized mathematics that it verified – is licensed open-source.

While learning these skills, he also intensely studied mathematics, architecture, perspective and map drawing.

While mathematicians usually study them for their own sake, by doing so results may be obtained that find application outside the realm of mathematics.

While he showed an early aptitude for mathematics, teaching himself calculus while a teenager, he left school after the 9th grade to work on his parents ' farm.

While in Geneva, he devoted himself to the study of mathematics under Georges-Louis Le Sage, and acquired from Switzerland an intense love of liberty.