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 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 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.

Because individual classes of foods differ in their requirements for preservation, a number of methods have been developed over the years involving one or a combination of procedures such as dehydration, fermentation, salting, chemical treatment, canning, refrigeration, and freezing.

Because they have kept the faith of their medieval fathers, English Catholics have always strongly resented the charge of being `` un-English ''.

Because if you can't then nobody else can either, nobody else can have him.

`` Because maybe I won't have to wear it always.

Because I liked this sad person so much, I said, `` Will you have a drink with me ''??

Because anthropology developed from so many different enterprises ( see History of Anthropology ), including but not limited to fossil-hunting, exploring, documentary film-making, paleontology, primatology, antiquity dealings and curatorship, philology, etymology, genetics, regional analysis, ethnology, history, philosophy, and religious studies, it is difficult to characterize the entire field in a brief article, although attempts to write histories of the entire field have been made.

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

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 some have a prevision of the glory to come and others foretaste their suffering, the state of waiting is called " Particular Judgment ".

Because the beaks of giant squids have been found embedded within lumps of ambergris, scientists have theorised that the substance is produced by the whale's gastrointestinal tract to ease the passage of hard, sharp objects that the whale might have eaten.

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 this, its main stars have no particular pattern and it is devoid of bright deep-sky objects.

Because the technique has allegedly been used to improve breathing and stamina in general, advocates also claim that athletes, people with asthma, tuberculosis, and panic attacks have also found improvements.

In fact, Fitzmyer believes that the preface of Luke should only be “ the starting point in the discussion of the aim of Luke-Acts .” Because the author ’ s intended purpose for the Book of Acts is not that straightforward, scholars have put forth four main claims to address this.

Because field artillery mostly uses indirect fire the guns have to be part of a system that enables them to attack targets invisible to them in accordance with the combined arms plan.

Because these users have different needs, the presentation of financial accounts is very structured and subject to many more rules than management accounting.

Because of this, correct imports of DXF files have been difficult.

Because of these accidents, the various aviation authorities around the world have created set rules and guidance for those running and participating in air displays.

Because of this risk, patients prescribed clozapine may need to have regular blood checks to catch the condition early if it does occur, so the patient is in no danger.

Because individuals with albinism have skin that entirely lacks the dark pigment melanin, which helps protect the skin from the sun's ultraviolet radiation, their skin can burn more easily from overexposure.

Because of its magnitude, scientists formerly speculated that the gases released during the formation of the Deccan Traps played a role in the Cretaceous – Paleogene extinction event ( also known as the K-Pg extinction ), which included the extinction of the non-avian dinosaurs.

Because the position of Kajang between three major city ( Kuala Lumpur, Seremban and Putrajaya ), this city is included in Klang Valley or Greater Kuala Lumpur.

Because selection is performed on the individual level, families with two or more affected children would have a higher probability of becoming included in the study.

Because steam locomotives included one or more steam engines, they are sometimes referred to as " steam engines ".

Because the whole meaning of that phrase is much different from the meaning of words included alone, phraseology examines how and why such meanings come in everyday use, and what possibly are the laws governing these word combinations.

Because much of the land that constituted Pangaea was distant from the oceans, temperatures fluctuated greatly, and the interior of Pangaea probably included expansive areas of desert.

Because of its view of concepts as " open-ended " classifications that go well beyond the characteristics included in their past or current definitions, Objectivist epistemology rejects the analytic-synthetic distinction as a false dichotomy and denies the possibility of a priori knowledge.

Smith's set included " Gloria ", " Because the Night " and " People Have the Power.

Because it was originally a royal residence, the Palace included no purpose-built chambers for the two Houses.

Because Judaism forbids pronouncing the name outside the Temple in Jerusalem, the correct pronunciation of the Tetragrammaton may have been lost, as the original Hebrew texts only included consonants.

Because the band had not included any name in the return address, the rejection slip was simply addressed to " The Residents ".

Because he was unsure of his future direction, he included some chemical engineering courses in his curriculum and spent a summer touring chemical plants in Massachusetts and Maine.

Because he was dealing with confusing leaf forms, the Q. prinus and Q. rubra specimens actually included mixed foliage of more than one species.

Because the index of refraction is included, the NA of a pencil of rays is an invariant as a pencil of rays passes from one material to another through a flat surface.

Because it can produce sparks when wet and can start hundreds or thousands of fires when used correctly, ferrocerium is a common item included in survival kits.

Because of " non-disclosure clauses " which may have been included in the fraudulent contract, reporting of the scam may be delayed until the victim becomes certain he has been cheated.

Because wild boar are included in the Dangerous Wild Animals Act 1976, certain legal requirements have to be met prior to setting up a farm.

Because of the Hindu traditions of Vedanta and Upanishads, and the prominent Hindu theological perspective that there is a single Reality ( Brahman ) from which the world arises, Hindus eventually have been included as dhimmis.

Because saints ' lives are often included many miracle stories, " legend " in a wider sense came to refer to any story that is set in a historical context but that contains supernatural or fantastic elements.

Because of the assumption that only one worker per family would be permitted to work under the proposed program, this total of 5. 15 million was further reduced by 1. 6 million — the estimated number of workers who were members of families which included two or more employable persons.

Because of this systemic approach UAS have been not included in the United States Munitions List Category VIII – Aircraft and Associated Equipment.

Because some of the new boroughs or districts covered areas much wider than the previous city, this had the effect that city status was awarded to a number of local government districts which were not themselves towns and included a number of towns and villages outside the urban areas from which the districts took their names, for example the cities of Bradford, Leeds and Winchester.

Because the film starred a crooner, Martin, and a teen idol, Nelson, Hawks included three songs in the soundtrack.

Because the vas deferens deposits seminal fluid into the prostatic urethra, and secretions from the prostate gland itself are included in semen content, prostate cancer may also cause problems with sexual function and performance, such as difficulty achieving erection or painful ejaculation.