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Page "Axiom of choice" ¶ 107
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We and will
We, in our country, think of war as an external threat which, if it occurs, will not be primarily of our own doing.
We will recall that the still confident liberals of the Truman administration gathered with other Western utopians in San Francisco to set up the legal framework, finally and at last, to rationalize war -- to rationalize want and fear -- out of the world: the United Nations.
We therefore leave the writer to the enjoyment of the unenvied reputation which the personal abuse he has heaped on us will entitle him to from the low and vulgar herd to which he belongs ''.
We hope that he will execute it in a manner that will entitle him to credit ''.
We may further grant to those of her ( Poetry's ) defenders who are lovers of poetry and yet not poets, the permission to speak in prose on her behalf: let them show not only that she is pleasant but also useful to States and to human life, and we will listen in a kindly spirit ; ;
We veterans acknowledge the fact that as time passes the demand for medical care at VA hospitals will grow proportionately as age fosters illness.
We feel that The Detroit News is to be complimented upon arranging for articles on these subjects and we hope that it will continue to provide material along wholesome lines.
We will know, and He will know, to whom it is rendered, what the birds would ask:
We now have to think not only of our national security but also of the future generations who will suffer from any tests we might undertake.
We welcome this able brief for the negative as part of a many-sided discussion of the Atlantic Common Market which JNR will be continuing in our pages.
We will have righteousness ''!!
We will not yield to the demands of Bern ''!!
We all seek the same thing through different ways -- an end to this long night of two thousand years of darkness and unspeakable abuses which will continue to plague us until the Star of David flies over Zion ''.
We must ask ourselves which of the two alternatives will help the commuter -- the two-way B. & O. - C. & O. merger, or the three-way New York Central - B. & O. - C. & O. merger.
We should hope that peace corps projects will be truly international and that our citizens will find themselves working alongside citizens of the host country and also volunteers from other lands.
We are initiating research on the use of solid state materials for infrared detection using a method which will not require cooling of materials to attain high sensitivity.
We will then occupy the new plant under lease, with an option to purchase.
We believe that these improved facilities will contribute income and effect savings which will fully justify the investment.
`` We, the Subscribers, do agree, that as soon as a convenient Number of Persons have subscribed to this, or a similar Writing, We will present a petition to the Hon'ble General Court of the Commonwealth of Massachusetts, praying for an Act incorporating into a Body politic the subscribers to such Writing with Liberty to build such a Bridge, and a Right to demand a Toll equal to that received at Malden Bridge, and on like Terms, and if such an Act shall be obtained, then we severally agree each with the others, that we will hold in the said Bridge the several shares set against our respective Names, the whole into two hundred shares being divided, and that we will pay such sums of Money at such Times and in such Manners, as by the said proposed Corporation, shall be directed and required ''.

We and abbreviate
We might abbreviate this colloquially to ' It's gonna rain '.
We will abbreviate this data by ( A, C, f, g, h ).

We and set
We of the liberal-led world got all set for peace and rehabilitation.
We feel uncomfortable at being bossed by a corporation or a union or a television set, but until we have some knowledge about these phenomena and what they are doing to us, we can hardly learn to control them.
We set up the Lloyd's Neck school, worked out its curriculum, and taught there.
We have set up a central R & D department, as well as engineering-management departments -- about 80 people working on problems related to those of our plants.
We turn now to the set of tangent points on the graph.
We first define a function b{t} as follows: given the set of squares such that each has three corners on C and vertex at t, b{t} is the corresponding set of positive parametric differences between T and the backward corner points.
We may now take up for consideration a hard case which seems to require either no action employing economic pressure or else action that would seem to violate the principles set forth above.
We met at Maxine's and decided we were set to stay as long as it took, into or even through the evening, to talk things out.
We also allow for an empty set, often denoted Ø and sometimes: a set without any members at all.
We just sold our farms and set out north-westwards to find a new home.
Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.
She lost her job on The Dinah Shore Show when, as she said, " We were shooting all night, and into the next day, and time just got away from me, and I didn't realize that I was supposed to be on the set working as Dinah's double on her show, Chevy Theatre.
Representable functors: We can generalize the previous example to any category C. To every pair X, Y of objects in C one can assign the set Hom ( X, Y ) of morphisms from X to Y.
We are interested in the following set of continuous functions called loops with base point x < sub > 0 </ sub >.
We define the kernel of h to be the set of elements in G which are mapped to the identity in H
The ( unique ) representable functor F: → is the Cayley representation of G. In fact, this functor is isomorphic to and so sends to the set which is by definition the " set " G and the morphism g of ( i. e. the element g of G ) to the permutation F < sub > g </ sub > of the set G. We deduce from the Yoneda embedding that the group G is isomorphic to the group
" I think the biggest black mark against our management to date is the Cukor situation and we can no longer be sentimental about it .... We are a business concern and not patrons of the arts ..." Cukor was relieved of his duties, but he continued to work with Leigh and De Havilland off the set.

We and theory
We may thus trace the notion of individual autonomy from its manifestation in religious practice and theological reflection through practical politics and political theory into literature and the arts.
We then outline the theory of the interaction of paramagnetic dipoles with nuclei and show that the theory is in excellent agreement with experiment.
We should expect that general phonologic theory should be as adequate for tone as for consonants and vowels, but it has not been.
We have been using the word `` public '' in quotation marks, that is, in its vernacular connotation with reference to the odd-lot index theory.
We believe, however, that such a theory is possible.
Along with her work as a writer of prose fiction, Russ was also a playwright, essayist, and author of nonfiction works, generally literary criticism and feminist theory, including the essay collection Magic Mommas, Trembling Sisters, Puritans & Perverts ; How to Suppress Women's Writing ; and the book-length study of modern feminism, What Are We Fighting For ?.
Carlyle notes: " There is no change in political theory so startling in its completeness as the change from the theory of Aristotle to the later philosophical view represented by Cicero and Seneca .... We think that this cannot be better exemplified than with regard to the theory of the equality of human nature.
We are now controlled not by binding extra-linguistic value paradigms defining notions of collective identity and ultimate purpose, but rather by our automatic responses to different species of " language games " ( a concept Lyotard imports from JL Austin's theory of Speech Acts ).
We do not know how these things happen, but the theory tells us about the probabilities of these things happening.
We see then that radar, like indeed all macro-scale entities, is profoundly impacted by quantum theory.
We are not able to see how the prohibition of teaching the theory that man has descended from a lower order of animals gives preference to any religious establishment or mode of worship.
We can use the three-dimensional theory to solve this problem if we regard u as a function in three dimensions that is independent of the third dimension.
We don't assume that the simpler theory is correct and the more complex one false.
We know from experience that more often than not the theory that requires more complicated machinations is wrong.
We now introduce the idea of the Aspiration level as introduced by Herbert Simon and developed in economics by Richard Cyert and James march in their 1963 book " A Behavioral theory of the firm ".
( We developed ) a theory to explain how solar protons can diffuse inward and gain energy in the Earth's magnetic field.
Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.
The essence of antiquarianism is a focus on the empirical evidence of the past, and is perhaps best encapsulated in the motto adopted by the 18th-century antiquary, Sir Richard Colt Hoare, " We speak from facts not theory ".
Another theory is that there may be a " gentlemen's agreement " in place ; i. e. " We won't jam yours if you don't jam ours ".
We can construct a classical continuous random field that has the same probability density as the quantum vacuum state, so that the principal difference from quantum field theory is the measurement theory ( measurement in quantum theory is different from measurement for a classical continuous random field, in that classical measurements are always mutually compatible — in quantum mechanical terms they always commute ).

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