Because these two definitions can be transformed simply by into the other, some formulae have this alternatingly (- 1 )< sup > n </ sup >- term and others not depending on the context, but it is not possible to decide in favor of one of these definitions to be the correct or appropriate or natural one ( for the abstract Bernoulli numbers ).

Because abstract algebra studies sets endowed with operations that generate interesting structure or properties on the set, functions which preserve the operations are especially important.

Because of the complex and abstract nature of love, discourse on love is commonly reduced to a thought-terminating cliché, and there are a number of common proverbs regarding love, from Virgil's " Love conquers all " to The Beatles ' " All You Need Is Love ".

Because of their nature, cards are well suited for abstract games, as opposed to the simulation aspects of wargames.

Because lighting design is much more abstract than costume or scenic design, it is sometimes difficult for the lighting designer to accurately convey his ideas to the rest of the production team.

Because of her work's added spiritual dimension, which became more and more dominant after 1967, she preferred to be classified as an abstract expressionist.

Because of his development of the concept of a " one god greatest among gods and men " that is abstract, universal, unchanging, immobile and always present, Xenophanes is often seen as one of the first monotheists, in the Western philosophy of religion, although the quotation that seems to point to Xenophanes's monotheism also refers to multiple " gods " who the supreme God is greater than.

Because an abstract summarizes an article, it is very useful for either browsing or keyword searching.

Because the concepts in physics and politics are at times very complicated or very abstract, Frayn uses several controlling images to better relate certain ideas to his audience.

Because humans have parts of happiness, happiness is concrete and not abstract.

Because these four symbols can be named and easily identified as everyday, concrete objects (" apple ", " house ", " window ", and " ring "), they can be recognized at an earlier age than abstract letters or numbers can be.

Because community not severalty of property is the law of nature no man can assert an absolutely unalterable right to what is his.

Because of the holistic nature of anthropological research, all branches of anthropology have widespread practical application in diverse fields.

Because of the quantum mechanical nature of the electrons around a nucleus, atomic orbitals can be uniquely defined by a set of integers known as quantum numbers.

Because virtually all extant written material on Arianism was written by its opponents, the nature of Arian teachings is difficult to define precisely today.

Because of his bellicose nature Albert received the cognomen Alcibiades after his death ; during his lifetime Albert was known as Bellator ( the Warlike ).

Because of its high chemical reactivity barium is never found in nature as a free element.

Because of his special status due to the virgin birth and his pure, unselfish nature, Jesus voluntarily faced his struggle in Gethsemane, death, resurrection, and ascension to show humanity that no phase of mortal existence was beyond God's redeeming love.

Because of his frequent association with creatures, scholars often describe Cernunnos as the " Lord of the Animals " or the " Lord of Wild Things ", and Miranda Green describes him as a " peaceful god of nature and fruitfulness ".

Because Capra's films often carry a message about basic goodness in human nature, and show the value of unselfishness and hard work, his wholesome, feel-good themes have led some to term his style " Capra-corn.

Because their text-only nature sidestepped the problem of writing for the widely divergent graphics architectures of the day, interactive fiction games were easily ported across all the popular platforms, even those such as CP / M not known for gaming or strong graphics capabilities.

Because of the controversial nature of Hoover's legacy, there have been periodic proposals to rename it by legislation proposed by both Republicans and Democrats in the House and Senate.

Because of its high reactivity, lithium never occurs freely in nature, and instead, only appears in compounds, which are usually ionic.

Because the rivers and streams have such steep gradients and are so fast moving, they are erosive instead of depository in nature.

Because of the anarchistic nature with which the groups sprang up, some jokingly referred to ALT standing for " Anarchists, Lunatics and Terrorists " ( a backronym ).

Because of the plant's deep secrecy and the difficult nature of the production process, it took from January 1940 until June 1942 for the plant to become fully operational.

Because of the extent of human influence, the boundaries between what humans regard as nature and " made environments " is not clear cut except at the extremes.

Because of the highly reactive nature of potassium metal, it must be handled with great care, with full skin and eye protection and preferably an explosion-resistant barrier between the user and the metal.

Drawbacks: Because of the nature of the pump, the clearance between the rotating pump and the outer edge must be very close, requiring that it rotates at a slow, steady speed.

Because of their nature, they rely on sight more than hearing, contrary to homophonic puns.

Because the ludi were religious in nature, it was appropriate for the Romans to set up this temporary stage close to the temple of the deity being celebrated.

Because of its high-impact nature, many injuries are associated with running.

Because of the very large nature of such roofs, it is essential that the outer skin is of a highly impermeable material.

Because of the controversial nature of this topic various studies yielded different results.

Because traits held to be due to sexual selection often conflict with the survival fitness of the individual, the question then arises as to why, in nature, in which survival of the fittest is considered the rule of thumb, such apparent liabilities are allowed to persist.

Because he loved Verdi ’ s music, Barezzi invited Verdi to be his daughter Margherita's music teacher, and the two soon fell deeply in love.

Because its main purpose was the presentation of live music, the hall needed a design focused not only on public access and exterior aesthetics, but also acoustics.

Because it spans music from Ragtime to the present day – over 100 years now – jazz can be very difficult to define.

Because of this, Postmodern music is mostly defined in opposition to modernist music, and a work can either be modernist, or postmodern, but not both.

Because of its complex history and tendency to borrow from other musical and cultural forms, it has been argued that " it is impossible to bind rock music to a rigidly delineated musical definition.

Because music written for early trumpets required the use of a different trumpet for each key — they did not have valves and therefore were not chromatic — and also because a player may choose to play a particular passage on a different trumpet from the one indicated on the written music, orchestra trumpet players are generally adept at transposing music at sight, sometimes playing music written for the B trumpet on the C trumpet, and vice versa.

Because they were suspicious of the music business in general, the Replacements had not signed a written contract with Twin / Tone Records.

Because of an extended stay in rehab, his performance at Snowbombing, a week-long winter sports and music festival held in the Austrian ski resort of Mayrhofen, was cancelled – with the slot being filled by 2ManyDJs.

Because of this, much of the music was performed in environments that were more constrained compared to the flourishing times of the Renaissance and Baroque Era's.

Because of the tempo of the music, the theme gained popularity in the UK with followers of Northern soul and was popular on dance floors in the 1970s.

Because of the longer measures, they are longer than the reel and the light jig, with the same number of bars to the music.

Because obtaining the rights to use the music would have been expensive, most stage versions, and the film, have Martha sing to the tune of " Here We Go Round the Mulberry Bush ".

Because Gilbert and Sullivan shared his vision of increasing the quality and respectability of English musical theatre, and so broadening its audience through the promotion of well-crafted English light operas, Carte gave them wider authority as director and music director than was customary at that time.

Because music often plays an important part in the performance of the liturgy, cathedrals generally have a pipe organ to accompany the choir.

Because the vast majority of these broadcasts contain nothing but the recitation of blocks of numbers, in various languages, with occasional bursts of music, they have become known colloquially as " Number Stations ".

Because of his discouragingly minor role in the band, and under the pressure of The Mundanes ' unsuccessful search for success, Linnell began recording music with John Flansburgh, though his family did not support the transition from what they considered to be a more professional band to an experimental one.

Because it breaks so many of rock's conventions at once, Beefheart's music has always been more influential than popular.

Because a condition of the offer was that the opera should be the composer's first publicly staged work, Bizet hurriedly withdrew La guzla from production and incorporated parts of its music into the new opera.

Because of this, our definition of what music technology encompasses continually expands.