`` We know Penny spent some -- and Carmer must have dropped a few dollars getting that load on ''.

`` We have now a national character to establish '', Washington wrote in 1783.

We have ample light when the sun sets ; ;

We have staved off a war and, since our behavior has involved all these elements, we can only keep adding to our ritual without daring to abandon any part of it, since we have not the slightest notion which parts are effective.

We are forced, in our behavior towards others, to adopt empirically successful patterns in toto because we have such a minimal understanding of their essential elements.

We showed them to each other and said `` Would you have guessed ''??

A Yale historian, writing a few years ago in The Yale Review, said: `` We in New England have long since segregated our children ''.

We hear equally fervent concern over the belief that we have not enough generalists who can see the over-all picture and combine our national skills and knowledge for useful purposes.

We have proved so able to solve technological problems that to contend we cannot realize a universal goal in the immediate future is to be extremely shortsighted, if nothing else.

We must believe we have the ability to affect our own destinies: otherwise why try anything??

We have recourse to the scientifically-trained specialist in the laboratory.

We must not forget, to be sure, that free discussion and debate have produced beneficial results.

We have so completely entered the child's fantasy that his illness and his death are the plausible and the necessary conclusion.

We experience a vague uneasiness about events, a suspicion that our political and economic institutions, like the genie in the bottle, have escaped confinement and that we have lost the power to recall them.

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 have nothing to hide under a bushel.

We already have the only one of its kind ''.

We may also recognize cases in which the poets have influenced the philosophers and even indirectly the scientists.

We must, therefore, have a look at the new archaeological material and re-examine the literary and place-name evidence which bears upon the problem.

`` We have just returned from Roswell, N.M., where we were defeated, 34 to 9 '', the young man noted.

`` We have a tremendous amount of talent -- but we lack cohesion ''.

We in East Greenwich have the example of two neighboring communities, one currently utilizing double sessions in their schools, and the other facing this prospect next year.

We have far less to fear in the migrant family than we have in the migrant developer under these conditions.

We shall show that the polynomials Af behave in the manner described in the first paragraph of the proof.

We can call a person, a house, a symphony, a fragrance, and a mathematical proof beautiful.

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.

We approach the proof of Theorem 2 by successively restricting the class of all formulas φ for which we need to prove " φ is either refutable or satisfiable ".

We have proved that φ is either satisfiable or refutable, and this concludes the proof of the Lemma.

We have shown as a byproduct of the proof of monotonicity that.

We will now follow the strategy of David Hilbert ( 1862 – 1943 ) who gave a simplification of the original proof of Charles Hermite.

We now give an operator theoretic proof for the Cauchy – Schwarz inequality which passes to the C *- algebra setting.

Proof: We only give the proof in the simplified case ; the general case is similar.

We will now give the precise meaning of this statement as well as its proof.

We will go over a typical application of Zorn's lemma: the proof that every nontrivial ring R with unity contains a maximal ideal.

Dan Olinger, a professor at the fundamentalist Bob Jones University in Greenville said, “ We want to be good citizens and participants, but we ’ re not really interested in using the iron fist of the law to compel people to everything Christians should do .” Bob Marcaurelle, interim pastor at Mountain Springs Baptist Church in Piedmont, said the Middle Ages were proof enough that Christian ruling groups are almost always corrupted by power.

We have proven both lemmas and have completed the proof.

We will prove these things below ; let us first see an example of this proof in action.

We provide a sketch of a proof for the case where the underlying field of scalars is the complex numbers.

" We " in this sense often refers to " the reader and the author ," since the author often assumes that the reader knows certain principles or previous theorems for the sake of brevity ( or, if not, the reader is prompted to look them up ), for example, so that the author does not need to explicitly write out every step of a mathematical proof.

We include here a proof that DTIME ( f ( n )) is a strict subset of DTIME ( f ( 2n + 1 )< sup > 3 </ sup >) as it is simpler.

The proof is again by induction, this time on the number of colours c. We have the result for c =

We call a a witness for the compositeness of n ( sometimes misleadingly called a strong witness, although it is a certain proof of this fact ).

* Example: " We cannot wait for the final proof – the smoking gun – that could come in the form of a mushroom cloud.

We can easily generalize this proof to the case of quantum mechanical models.

" We " in this sense often refers to " the reader and the author ", since the author often assumes that the reader knows certain principles or previous theorems for the sake of brevity ( or, if not, the reader is prompted to look them up ), for example, so that the author does not need to explicitly write out every step of a mathematical proof.

We give a proof by induction.

First proof: Suppose forms a basis of ker T. We can extend this to form a basis of V:.