We shall prove that Af.

We can now prove several lemmas.

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 seek to prove that there exist two irrational numbers and such that

Say instead we wish to prove proposition p. We can proceed by assuming " not p " ( i. e. that p is false ), and show that it leads to a logical contradiction.

We prove the inequality

We prove that there exists ( x, y, z ) such that

We should prove that the angular velocity previously defined is independent from the choice of origin, which means that the angular velocity is an intrinsic property of the spinning rigid body.

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

We can prove the cancellation law easily using Euclid's lemma, which generally states that if an integer b divides a product rs ( where r and s are integers ), and b is relatively prime to r, then b must divide s. Indeed, the equation

In 1950, Time quoted Webb: " We don ’ t even try to prove that crime doesn ’ t pay ... sometimes it does " ( Dunning, 210 )

We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.

We shall prove the five lemma by individually proving each of the 2 four lemmas.

We prove that if an increasing sequence is bounded above, then it is convergent and the limit is.

We wish to prove that they are all the same color.

We cannot use Russia's methods, as they only and at best prove that the economy of an agrarian nation can be leveled to the ground ; Russia's thoughts are not our thoughts.

Jim Capaldi used this hiatus to record a solo album, Oh How We Danced, which would prove to be the beginning of a long and successful solo career.

We shall therefore now consider only arguments that prove the theorem directly for any matrix using algebraic manipulations only ; these also have the benefit of working for matrices with entries in any commutative ring.

We need to prove that some time class TIME ( g ( n )) is strictly larger than some time class TIME ( f ( n )).

We prove that R ( r, s ) exists by finding an explicit bound for it.

We now prove the result for the general case of c colours.

We have given to us a conception A uniting among its constituent marks two that prove to be contradictory, say M and N ; and we can neither deny the unity nor reject one of the contradictory members.

We wish to prove 4T < sup > 2 </ sup >

We do not intend to prove otherwise.

We are desperately in the need of such invention, for man is still very much at the mercy of man.

We consider a rural community as an assemblage of inhabited dwellings whose configuration is determined by the location and size of the arable land sites necessary for family subsistence.

We assume for this illustration that the size of the land plots is so great that the distance between dwellings is greater than the voice can carry and that most of the communication is between nearest neighbors only, as shown in Figure 2.

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 are reminded, however, that freedom of thought and discussion, the unfettered exchange of ideas, is basic under our form of government.

We know that much is made of the multiplicity and ambiguity of the identities that cluster around the key symbol of the Jew.

We saw it frequently afterward, but our suggestion for the very first encounter is near sunset.

In the rhyming catechism this doctrine is worded thus: `` In Adam's fall We sin-ned all ''.

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 find, in the first place, that the students overwhelmingly approve of higher education, positively evaluate the job their own institution is doing, do not accept most of the criticisms levelled against higher education in the public prints, and, on the whole, approve of the way their university deals with value-problems and value inculcation.

There is, of course, nothing new about dystopias, for they belong to a literary tradition which, including also the closely related satiric utopias, stretches from at least as far back as the eighteenth century and Swift's Gulliver's Travels to the twentieth century and Zamiatin's We, Capek's War With The Newts, Huxley's Brave New World, E. M. Forster's `` The Machine Stops '', C. S. Lewis's That Hideous Strength, and Orwell's Nineteen Eighty-Four, and which in science fiction is represented before the present deluge as early as Wells's trilogy, The Time Machine, `` A Story Of The Days To Come '', and When The Sleeper Wakes, and as recently as Jack Williamson's `` With Folded Hands '' ( 1947 ), the classic story of men replaced by their own robots.

We saw Giuseppe Berto at a party once in a while, tall, lean, nervous and handsome, and, in our opinion, the best novelist of them all except Pavese, and Pavese is dead.

We submit that this is a most desirable effect of the law -- and one of its principal aims.

We believe that autism, like so many other conditions of defect and deviation, is to a large extent inborn.

`` Dear Doctors: We learned this year that our older son, Daniel, is autistic.

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:

If it is not enough that all of our internationalist One Worlders are advocating that we join this market, I refer you to an article in the New York Times' magazine section ( Nov. 12, 1961 ), by Mr. Eric Johnston, entitled `` We Must Join The Common Market ''.

We out here don't see enough of the conference to know he is being abused.

We repeat, that the test of a violation of 7 is whether, at the time of suit, there is a reasonable probability that the acquisition is likely to result in the condemned restraints.