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 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 of its importance, and because the lack of price competition is well recognized, the industry is under considerable public pressure not to raise its price any more than could be justified by cost increases.

Because of lack of financing, the development of oil fields near Doba, originally due to finish in 2000, was delayed until 2003.

Because of the lack of worldwide knowledge about the order in general, very little is known about the order diversity.

Because they lack this key defence, only 0. 5 % of cane toads are estimated to reach adulthood.

Because of their physical similarity to humans a replicant must be detected by its lack of emotional responses and empathy to questions posed in a Voight-Kampff test.

Because of his lack of commercial success, Bowie was forced to try to earn a living in different ways.

Because of their lack of hydrogen-bond-donating ability, esters do not self-associate.

Because of this, they lack referential transparency, i. e. the same language expression can result in different values at different times depending on the state of the executing program.

Because of the lack of subsidies and a need to reduce expenditures, many social programs in Hungary had to be cut in an attempt to lower spending.

Because of severe shortages in weapons and equipment and lack of training, members of the Volkssturm were poorly prepared for combat, and about 175, 000 of them lost their lives in the final months of the war.

Because of the difficulty of manipulating metal and the lack of machine tools, the use of metal was kept to a minimum.

Because it relies on volunteers and uses " rough consensus and running code " as its touchstone, results can be slow whenever the number of volunteers is either too small to make progress, or so large as to make consensus difficult, or when volunteers lack the necessary expertise.

Because of a lack of anti-tank weapons, German battleships used their guns to support the defenders of Kolberg until nearly all of the soldiers and civilians had been evacuated.

Because of its mountainous topography and lack of development, Laos has few reliable transportation routes.

Because the scripts used to write some Semitic languages lack vowel letters, unambiguous reading of a text might be difficult.

Because of the wide slew-range and lack of positive feedback, the response of all the open-loop level detectors described above will be relatively slow.

Because of the lack of topographic barriers within Paraguay, these opposite prevailing winds bring about abrupt and irregular changes in the usually moderate weather.

Because of the lack of scientific support, along with religious and prejudicial reasons phrenology never found a wide audience in Ireland.

Because of the lack of central authority in P2P networks, forces such as the recording industry, RIAA, MPAA, and the government are unable to delete or stop the sharing of content on P2P systems.

Because the key distinguishing characteristic Marsh noted for Pteranodon was its lack of teeth, any toothless pterosaur jaw fragment, wherever it was found in the world, tended to be attributed to Pteranodon during the late nineteenth and early twentieth centuries.

Because of their physical similarity to humans, a replicant must be detected by its lack of emotional responses and empathy to questions posed in a Voight-Kampff test.

Because of a lack of cement, mud was used as the mortar for many buildings, most of which had deteriorated into a state of ruin.

Because of the commercial failure of the machine and lack of support, particularly in Finland, Torvalds became very used to having to write his own software rather than relying on programs written by others.

Because of Skuld's lack of magic power, Noble Scarlet lacked the full unequivocal obedience an angel must have for her goddess.

Because Adorno believed that sociology needs to be self-reflective and self-critical, he believed that the language the sociologist uses, like the language of the ordinary person, is a political construct in large measure that uses, often unreflectingly, concepts installed by dominant classes and social structures ( such as our notion of " deviance " which includes both genuinely deviant individual and " hustlers " operating below social norms because they lack the capital to operate above: for an analysis of this phenomenon, cf.