Using Zorn's lemma, it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.

Because society needs people to do computing well, we must think of computing not only as a profession but also as a discipline.

Because of the special μ we picked, we may substitute dμ / dx for μ p ( x ), simplifying the equation to:

Because we were funny people it was going to be a funny film, but we wanted to get it right.

Because it is unitary, we can regard it as a symmetry operator.

Because it is usually more convenient to work with unrestricted integrals than restricted ones, we have chosen our normalizing constant to reflect this.

Because there was no distinct line between personal documents and those meant for publication, we frequently find in his letters both confidential messages and treatises meant for others besides the one to whom he was writing.

Because we have not included sufficiently complete axioms, though, nothing else may be deduced.

) Because our bodily involvement with things is always provisional and indeterminate, we encounter meaningful things in a unified though ever open-ended world.

Because they've exploited — we have seen the — we have seen the Nigger and Greaseball, we've seen the Chink, we've seen the slit-eyed dangerous Jap, we have seen the wily Filipino, we've seen everything but we never saw the Kike.

Because the soul's attention, while inhabiting a body, is turned so far away from its origin in the intelligible world, Proclus thinks that we need to make use of bodily reminders of our spiritual origin.

Because of the great distances to the farthest quasars and the finite velocity of light, we see them and their surrounding space as they existed in the very early universe.

Because these events are independent, we obtain the approximation:

Because we lack this essential background information, we are not justified in inferring that there exists an intelligent Deity who deliberately created a universe capable of sustaining life.

Because a tachyon always moves faster than light, we cannot see it approaching.

Because, when we get to the part about a particular decision that causes the tree to appear out of thin air, we draw a blank.

: Because we love our Vegemite

" Because we grew up on comic books and the Tolkien trilogy, one of the things we're interested in is bringing serial fiction to cinema ," Lana has said.

Because Bright's speeches were so much a part of him, there are long and numerous quotations, which, far from making the biography diffuse, help to give us the feel of the man.

Because God is what He is, the laws of the universe, material and spiritual, are what they are.

Because, honey, I thought silently, there are plenty of desert islands in every marriage -- long periods when you're hopelessly stranded, together.

Because administration of the forest highway system is a responsibility of the Secretary of Commerce with maintenance provided by the States and counties, this Development Program for the National Forests does not include estimates of the funds needed to maintain the forest highway system nor to construct the additions to it that are needed.

Because they are `` minority '' exercises and have but a limited appeal they soon find themselves in the limbo of the forgotten.

Because of this, it would appear inevitable that an increasing percentage of strategic missiles will seek self-protection in mobility -- at least until missile defenses are perfected which have an exceedingly high kill probability.

( Note: Because of light leakage from one ultraviolet source to another, the lights are switched by a commutator-like assembly rotated by a synchronous motor.

Because of their location, on the edge of the feed lot, fence-line bunks are not in the way of mechanical manure removal.

Because agricultural activities are seasonal and the areas of production and harvest of many foods are widely scattered geographically, and because of the high cost of transporting bulk food items any substantial distance to a central processing location, the use of large central processing stations, where low-cost radiation facilities approaching the megawatt range might be utilized, is inherently impracticable.

Because electrical forces ( the charge-excess ) are far more powerful than gravitation, the surface hydrogen atoms would shoot away from the sphere.

Because the levels themselves are random variables, some assumptions and the method of contrasting the treatments ( a multi-variable generalization of simple differences ) differ from the fixed-effects model.

Because constitutional claims are of great magnitude, appellate courts might be more lenient to review the claim even if it was not preserved.

Because of the ocean's great capacity to store and release heat, maritime climates are more moderate and have less extreme seasonal variations than inland climates.

Because of its simplicity, star hopping is a very common method for finding objects that are close to naked-eye stars.

Because CCD imagers are linear, image processing may be used to subtract away the effects of light pollution, which has increased the popularity of astrophotography in urban areas.

Because all clades are represented in the southern hemisphere but many not in the northern hemisphere, it is natural to conjecture that there is a common southern origin to them.

Because of their biological significance, amino acids are important in nutrition and are commonly used in nutritional supplements, fertilizers, and food technology.

Because of their relatively large mass, + 2 electric charge and relatively low velocity, alpha particles are very likely to interact with other atoms and lose their energy, so their forward motion is effectively stopped within a few centimeters of air.

Because of the tortuous terrain in places, villages and towns in the mountains — to which travel via motorized vehicles are of little use — are still located in the high Andes of Argentina, Bolivia, Peru, and Ecuador.

Because Ambrosius and Vortigern are shown in the Historia Brittonum as being in conflict, some historians have suspected that this preserves a historical core of the existence of two parties in opposition to one another, one headed by Ambrosius and the other by Vortigern.

Because of its elevation and distance from the coast, the Australian Capital Territory experiences four distinct seasons, unlike many other Australian cities whose climates are moderated by the sea.

Because of increasing anemia, triamcinolone, 8 mg. daily, was started on Feb. 23, 1958, and was continued until July, 1958.

Because water is incompressible and must remain within the confines of the bucket, this outward movement increases the depth of water at the larger radius, increasing the height of the surface at larger radius, and lowering it at smaller radius.

Because of the increasing costs of food imports to avoid mass-starvation in Germany, and with the danger of losing the entire nation to communism, the U. S. government abandoned the Morgenthau plan in September 1946 with Secretary of State James F. Byrnes ' speech Restatement of Policy on Germany.

Because of theological statements like this, many past Egyptologists, such as Siegfried Morenz, believed that beneath the polytheistic traditions of Egyptian religion there was an increasing belief in a unity of the divine, moving toward monotheism.

Because of Hund's rules, the first few electrons in a shell tend to have the same spin, thereby increasing the total dipole moment.

Because of his increasing interest in the social sciences, Manchester University created a new chair in Social Science ( 1948 – 58 ) for him.

Because of the increasing economic deprivation of Europe, Prokofiev returned to Russia in 1936.

Because of this, bartenders and restaurant owners began creating a variety of snacks to serve with sherry, thus increasing their alcohol sales.

Because of this belief in the stability of free-market economies they asserted that active demand management ( e. g. by the means of increasing government spending ) is unnecessary and indeed likely to be harmful.

Because the logarithm is a monotonically increasing function, the logarithm of a function achieves its maximum value at the same points as the function itself, and hence the log-likelihood can be used in place of the likelihood in maximum likelihood estimation and related techniques.

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 the temperature in the tropopause and lower stratosphere remains constant ( or slightly increases ) with increasing altitude, very little convective turbulence occurs at these altitudes.

Because of increasing concern surrounding Queen Elizabeth's safety, in 1584 Elizabeth's Privy Council signed a " Bond of Association " The identities of the six conspirators were nevertheless discovered, and they were taken prisoner by 15 August 1586.

Because the speaker is constantly moving either toward or away from the listener, however, the mechanism's rotation is constantly affecting the listener-perceived sound's wavelength by either " stretching " the wave ( increasing wavelength ) or " squeezing " it ( decreasing wavelength ) -- and because frequency, i. e., pitch, is inversely proportional to wavelength, such that increasing wavelength decreases frequency and vice versa, any listener for whom the speaker's motion changes the sound's perceived amplitude ( i. e., any listener whose distance from the speaker is changing ) must also perceive a change in frequency.

Because of the increasing popularity of NLP, scientific researchers began testing its theoretical underpinnings empirically, many of them showing a lack of empirical support for NLP's essential theories.

Because of increasing importance of shipbuilding industry some influential Bremen merchants, bankers and politicians decided in 1872 to establish a new and greater company on shares.

Because of the increasing traffic, president Vicente Fox announced the construction of a new, larger airport on in the municipalities of Texcoco and San Salvador Atenco, but when local violent protests aroused, the new airport was cancelled.

Because of the increasing number of students, in 1974 the first Reception Week for First Year Students (, OWEE ) was established, which became a TU Delft tradition since then.

Because of its connection with Exeter College and that college's increasing puritanism, a number of Exeter's tutors and scholars migrated to Hart Hall.

Because of increasing services and programs, the assistant principal position was reinstated.

; 358: Because of the increasing danger of Roman persecution, Hillel II creates a mathematical calendar for calculating the Jewish month.

Because of increasing urbanisation these had all been abolished by 1934.