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 her father's job required the family to move often, Flockhart and her brother grew up in several places including Illinois, Iowa, Minnesota, New Jersey, and Norwich, New York.

Because no one in the house paid attention to her singing she never got the feeling that any of them thought she had a good voice but after an initial rush of stage fright before her first solo, Gaynor's confidence in her singing grew.

Because the group chose to adopt celibacy and their members grew older, more work gradually had to be hired out.

Because of the silver ore deposits in the Erzgebirge, Zwickau developed in the 15th and 16th centuries and grew to be an important economic and cultural centre of Saxony.

Because of that, Heracles grew inimicious towards Hippocoön, killed him and reinstated Tyndareus.

Because of the wealth of natural resources found in Grant County, agriculture, ranching, and timber industries naturally grew with and contributed to the development of the county.

Because of its central location within the state and its abundant supply of water, Milledgeville grew rapidly into a bustling frontier settlement.

Because of the abundance of trees, the city grew quickly and was incorporated in 1889.

Because of the rapid industrial growth in Germany and the daily tides, two citizens of Hendrik-Ido-Ambacht started a ship breaking yard which grew into an industry resulting in the town becoming worldwide known as the " ship breaking village ".

Because of this, Susning grew and became Sweden's biggest and the world's next biggest wiki.

Because it lay on the trade route between Flanders and Brabant, the town prospered and grew into a city.

Because Amerike's coat of arms was similar to the flag later adopted by the independent United States, a legend grew that the North American continent had been named for him rather than for Amerigo Vespucci.

Because the only communist country fully prepared for modern technical warfare was the Soviet Union, Peng grew to see the Soviet Red Army as a model for the development of China's PLA.

Because Usenet grew rapidly, the limited capabilities and simplistic article storage scheme ( all articles were placed in a single disk directory and there was no facility for expiring old articles ) quickly made A News impractical to use.

Because of its location and depth, the Port grew rapidly with the introduction of steamships ; and then with the completion in 1825 of the Erie Canal New York became the most important transshipping port between the American interior and Europe as well as coastwise destinations.

Because of the criminal family's aid to Wo Mai, the city of Kai Shan to this day retains its autonomy and the ruling criminal family grew into what is known today as the Triad or Tsui Tong.

Because of the Empire's historical strength the United States had traditionally planned for a defensive war with it, and War Plan Red continued doing so even as American power grew to match Britain's.

Because Matsushita no longer felt challenged in his career, he soon grew dissatisfied with his job.

Because of its strategic location along important infrastructure the town grew rich because of flourishing trade.

" She has attributed her outspokenness to her upbringing in Romania under the totalitarian regime of Nicolae Ceaușescu: " Because I grew up in a country where there was no possibility of having an opinion, it makes me stronger now.

Because Xuan grew up as a commoner, he thoroughly understood the suffering of his people.

Because of its origins in the immediate post-war period, when electricity demand grew rapidly but plant and fuel availability was often unreliable, most of the industry saw its mission as to provide an adequate and secure electricity supply, or " to keep the lights on " as they put it, rather than necessarily pursuing the cheapest generation route.

Because of this influx of well-to-do planters an aristocratic society grew earlier than in areas to the south.

Because of the constraints of the rivers and marshland Wareham grew little during the 20th century, while nearby towns, such as Poole, grew rapidly.