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Page "Countable set" ¶ 11
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By and definition
By accepted definition, a 1-ton conditioner will provide 12,000 BTU of cooling in one hour.
By the Brønsted-Lowry definition, any compound which can easily be deprotonated can be considered an acid.
By definition it does not cover problems whose solution are unknown or have not been characterised formally.
By definition a multilinear map is alternating if it vanishes whenever two of its arguments are equal.
By this definition, if previous versions ( N-1, N-2, etc.
* By the definition of addition and scalar multiplication of linear functionals in the dual space,
By definition, where a director enters into a transaction with a company, there is a conflict between the director's interest ( to do well for himself out of the transaction ) and his duty to the company ( to ensure that the company gets as much as it can out of the transaction ).
By legal definition, all semi-highways are expressways.
By 1963 – 4 Gödel would disavow Herbrand – Gödel recursion and the λ-calculus in favor of the Turing machine as the definition of " algorithm " or " mechanical procedure " or " formal system ".
By contrast, a dictionary definition has additional details, typically including an etymology showing snapshots of the earlier meanings and the parent language.
By his own admission, Hubbard made what he considered was one of the greatest mistakes of his life when he used the biological definition of engram as a " trace on a cell ", which was not in line with the proper biological definition.
By definition, this classifies it as both a river and a strait — a strait being a narrow passageway connecting two large bodies of water.
Let f and g be any two elements of G. By virtue of the definition of G, = and =, so that =.
By definition, it is the amount of energy gained by the charge of a single electron moved across an electric potential difference of one volt.
At standard temperature, pressure and concentration conditions, the cell's emf ( measured by a multimeter ) is 0. 34 V. By definition, the electrode potential for the SHE is zero.
By definition, equality follow a number of " equivalence relations ", including ( a ) reflexive ( i. e. ), ( b ) symmetric ( i. e. if then ) ( c ) transitive ( i. e. if and then ).
By definition, a and b can be written as multiples of c: a = mc and b = nc, where m and n are natural numbers.
By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two.
By an abuse of the definition, a particular formal language is often thought of as being equipped with a formal grammar that describes it.
By definition, maps objects and morphisms identically to.
By definition, granite is an igneous rock with at least 20 % quartz by volume.
By definition, these clouds must have a v < sub > lsr </ sub > greater than 90 km s < sup >− 1 </ sup >, where v < sub > lsr </ sub > is the local standard rest velocity.
By definition, there was only one " catholic " or " universal " Church.

By and set
By fixing the tax rate in advance of spending, upper limits are set on expenditures.
By such innocent actions are human tragedies sometimes set in motion.
By adding a systematic analysis with symbols to the typed transcripts of interviews, they have supplied a new set of techniques for the therapist.
By and large, Robert McEnroe's adaptation of Maurice Walsh's film, `` The Quiet Man '', provides the entertainment it set out to, and we have a lively musical show if not a superlative one.
By the 27th century BC Egyptian writing had a set of some 24 hieroglyphs which are called uniliterals, to represent syllables that begin with a single consonant of their language, plus a vowel ( or no vowel ) to be supplied by the native speaker.
By taking up on the bow cable the stern anchor can be set.
By 1957, he set this subject aside in order to work in algebraic geometry and homological algebra.
By 16: 00, Alexander and Swiftsure were also in sight, although some distance from the main British fleet, and Brueys gave orders to abandon the plan to remain at anchor and instead for his line to set sails, although Blanquet protested the order on the grounds that there were not enough men aboard the French ships to both sail the ships and man the guns.
By far the most visible and obvious power of many modern central banks is to influence market interest rates ; contrary to popular belief, they rarely " set " rates to a fixed number.
Additional milieu were provided by Chaosium with the release of Dreamlands, a boxed supplement containing additional rules needed for playing within the Lovecraft Dreamlands, a large map and a scenario booklet, and Cthulhu By Gaslight, another boxed set which moved the action from the 1920s to the 1890s.
By the beginning of the Warring States, progress in astronomy and mathematics allowed the creation of calculated calendars ( where intercalary months and days are set by a rule, and not arbitrarily ).
By local coordinates is meant a set of coordinates that travel with the particle,
By August they had captured Stanleyville and set up a rebel government there.
By the 1930s, Ben Duncan and others popularized streamlined trap kits leading to a basic four piece drum set standard: bass, snare, tom-tom, and floor tom.
By the time of the Eighth Doctor audio play Terror Firma ( set after Remembrance ), Davros is commanding a Dalek army which has successfully conquered the Earth.
By using a set of n flexible rods, one can arrange that every rod touches every other rod.
* 1502 10 July – By a Royal Warrant passed in Toledo by Isabella I of Castile, Gibraltar was granted its coat of arms: " An escutcheon on which the upper two thirds shall be a white field and on the said field set a red castle, and below the said castle, on the other third of the escutcheon, which must be a red field in which there must be a white line between the castle and the said red field, there shall be a golden key which hangs by a chain from the said castle, as are here figured ".
By proving that there are ( infinitely ) many possible sizes for infinite sets, Cantor established that set theory was not trivial, and it needed to be studied.
By taking the intersection of p ( 1 ), p ( 2 ), p ( 3 ),... he formed p ( ω ), and then he noticed that p ( ω ) had a set of limit points p ( ω + 1 ), and so on.
By setting the story in the ruined abbey, Radcliffe was able to use architecture to draw on the aesthetic theories of the time and set the tone of the story in the minds of the reader.
By 2006, such was the confusion from these multiple Acts, each amending the others ( and not all of which were ever actually commenced and thus were in the public record but not enforced as actual legislation ); and the amendments of Irish firearms legislation by other Acts ranging from the Wildlife Acts ( mostly relating to hunting law ) to the Road Traffic Acts ( relating to how and where firearms could be transported ) and others ; the large amount of secondary legislation ( Statutory Instruments, which set out regulations, the design of application forms for licences and so forth, as well as the details of when various parts of the Acts came into force ); as well as the introduction of EU firearms law into the canon of Irish legislation ; led the Irish Law Reform Commission to recommend that all the extant legislation be restated a legal process by which all the existing primary and secondary legislation would be read as one and a single document produced as the new Firearms Act ( and all prior Acts would be repealed ).
By pursuing exclusive publication rights for his own works, he set one of the most important early precedents for regarding music as the intellectual property of the composer.
By the mid-18th century decline had set in because of several economic factors.
* Instruction set reference for 6809 / 6309 ( PDF ) By Chris Lomont

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