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It is possible to prove many theorems using neither the axiom of choice nor its negation ; such statements will be true in any model of Zermelo – Fraenkel set theory ( ZF ), regardless of the truth or falsity of the axiom of choice in that particular model.
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is and possible
It is possible, although highly doubtful, that he killed none at all but merely let his reputation work for him by privately claiming every unsolved murder in the state.
It is also possible, but equally doubtful, that he actually shot down the hundreds of men with which his legend credits him.
`` Now that Bruno Walter is virtually in retirement and my dear friend Dimitri Mitropoulos is no longer with us, I am probably the only one -- with the possible exception of Leonard Bernstein -- who has this special affinity for and champions the works of Bruckner and Mahler ''.
Even in domains where detailed and predictive understanding is still lacking, but where some explanations are possible, as with lightning and weather and earthquakes, the appropriate kind of human action has been more adequately indicated.
Within this notion clarity is possible, but for us who are neither Greek nor Jansenist there is not such clarity.
Mimesis is the nearest possible thing to the actual re-living of experience, in which the imagining person recovers through images something of the force and depth characteristic of experience itself.
Whitehead contends that the human way of understanding existence as a unity of interlocking and interdependent processes which constitute each other and which cause each other to be and not to be is possible only because the basic form of such an understanding, for all its vagueness and tendency to mistake the detail, is initially given in the way man feels the world.
The first of two possible variations on this theme is symbolized by Mickey Spillane's Mike Hammer.
All we want from Dr. Huxley's statement is the feeling that this is an open world, in the view of the best scientific opinion, with practically no directional commitments as to what may happen next, and no important confinements with respect to what may be possible.
In the range and variety of characters who, in their literary lives, get along all right with life styles one never imagined possible, there is an implicit lesson in differentiation.
It is possible that the study of literature affects the conscience, the morality, the sensitivity to some code of `` right '' and `` wrong ''.
It is possible that the idea of enrichment of emotion is a fifth idea.
It is at least possible that the capacity to postpone gratification is developed as well as expressed in a continuous and guided exposure to great literature.
Most students of literature, whether they call themselves scholars or critics, are ready to argue that it is possible to understand literary works as well as to enjoy them.
In looking back over the volumes, it is possible to find errors of interpretation, some of which were not so evident at the time of writing.
Says he, `` I may never imagine that in the struggle between personal and supra-personal responsibility it is possible to make a compromise between the ethical and the purposive in the shape of a relative ethic ; ;
Fortunately, it is possible to be somewhat more concrete and factual in diagnosing the involvement of values in education.
But when the situation was so complicated that even Nogaret, one of the principal actors in the drama, could misinterpret the pope's motives, it is possible that Othon and his companions, equally baffled, attributed their difficulties to a more immediate cause.
It is no longer possible to say that a sceptical attitude towards the received accounts of the invasions almost automatically produces a `` shore occupied by '' interpretation.
is and prove
Therefore, what we must prove or disprove is that there were Saxons, in the broad sense in which we must construe the word, in the area of the Saxon Shore at the time it was called the Saxon Shore.
Today the recreational boating scene is awash with heartening statistics which prove the enormous growth of that sport.
It is possible that especially large anacondas will prove to belong to subspecies limited to a small area.
The theorem which we prove is more general than what we have described, since it works with the primary decomposition of the minimal polynomial, whether or not the primes which enter are all of first degree.
-- On the basis of a differentiability assumption in function space, it is possible to prove that, for materials having the property that the stress is given by a functional of the history of the deformation gradients, the classical theory of infinitesimal viscoelasticity is valid when the deformation has been infinitesimal for all times in the past.
What determines the morality, they state, is not the means used, but the motive In general, the means ( excluding abortion ) that prove most effective are considered the most ethical.
Action located where the evil is concentrated will prove most decisive and is most clearly legitimate.
This increase in the `` threshold '', as the conventional forces strengthening is called, will prove one of the alliance's most difficult problems in the months to come.
More than 300 teenagers last Sunday proved there is and as many more are expected to prove it again for Jim Kern and his wife Lynn from 4 to 8 p.m. Sunday at First Presbyterian Church.
In searching for clues which might lead us to a fresh apprehension of the reality of spirit, the close connection between spirit and community is likely to prove the most fruitful.
Instead -- and not just to prove my objectivity -- I hasten to report that it's a highly amusing film which probably does a fairly accurate job of reporting on the Easter vacation shenanigans of collegians down in Fort Lauderdale, and that it seems to come to grips quite honestly with the moral problem that most commonly vexes youngsters in this age group -- that is to say, sex.
But chains of movements are not necessarily communicative, and it is in the realm of communication that the works prove disappointing.
`` You're working up to something, and if you don't watch out you'll ruin your whole life one of these days just to prove that the Abernathy family is superior to everything, even a depression ''.
`` The only thing that worries me is how I'm going to prove it '', Eugenia said.
In order for the appeal to succeed, the appellant must prove that the lower court committed reversible error, that is, an impermissible action by the court acted to cause a result that was unjust, and which would not have resulted had the court acted properly.
If a defendant has been convicted and can prove that his lawyer did not adequately handle his case and that there is a reasonable probability that the result of the trial would have been different had the lawyer given competent representation, he is entitled to a new trial.
Chaitin prefaces his definition with: " I'll show you can't prove that a program is ' elegant '"— such a proof would solve the Halting problem ( ibid ).
" In general, it is impossible to prove that F exists without the axiom of choice, but this seems to have gone unnoticed until Zermelo.
For example, the Banach – Tarski paradox is neither provable nor disprovable from ZF alone: it is impossible to construct the required decomposition of the unit ball in ZF, but also impossible to prove there is no such decomposition.
is and many
Too many people think that the primary purpose of a higher education is to help you make a living ; ;
As it is in so many affairs of the heart, a man and a woman meet and something clicks.
I want the room in the attic prepared for him He is a most unusual lad, quite precocious in many ways.
There is much truth in both these charges, and not many Bourbons deny them.
They are huge areas which have been swept by winds for so many centuries that there is no soil left, but only deep bare ridges fifty or sixty yards apart with ravines between them thirty or forty feet deep and the only thing that moves is a scuttling layer of sand.
Isfahan became more of a legend than a place, and now it is for many people simply a name to which they attach their notions of old Persia and sometimes of the East.
On Fridays, the day when many Persians relax with poetry, talk, and a samovar, people do not, it is true, stream into Chehel Sotun -- a pavilion and garden built by Shah Abbas 2, in the seventeenth century -- but they do retire into hundreds of pavilions throughout the city and up the river valley, which are smaller, more humble copies of the former.
All but the most rabid of Confederate flag wavers admit that the Old Southern tradition is defunct in actuality and sigh that its passing was accompanied by the disappearance of many genteel and aristocratic traditions of the reputedly languid ante-bellum way of life.
The street that is full now of traffic and parked cars then and for many years drowsed on an August afternoon in the shade of the curbside trees, and silence was a weight, almost palpable, in the air.
After how many generations is such wealth ( mounting all the while through the manipulations of high finance ) purified of taint??
The same command is repeated as many times as there are levels in rank from general to corporal.
Of course, there must be clarity: a single distinct impression is more valuable than many fuzzy ones.
If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.
There is evidence to suggest, in fact, that many authors of the humorous sketches were prompted to write them -- or to make them as indelicate as they are -- by way of protesting against the artificial refinements which had come to dominate the polite letters of the South.
It seems quite obvious that all the really difficult tasks of human beings arise from the fact that man is not one, but many.
Each man, that is, is both one and many.
The men who speculate on these institutions have, for the most part, come to at least one common conclusion: that many of the great enterprises and associations around which our democracy is formed are in themselves autocratic in nature, and possessed of power which can be used to frustrate the citizen who is trying to assert his individuality in the modern world ''.
Third, the United States is pressing forward in the development of large rocket engines to place vehicles of many tons into space for exploration purposes.
Outstanding among these is the idea of human nature itself, including the many definitions that have been advanced over the centuries ; ;
The other is that the charge for cabanas and parasols, though modest from an American point of view, still is a little high for many Athenians.
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