If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

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.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

This is a Cauchy sequence of rational numbers, but it does not converge towards any rational limit: If the sequence did have a limit x, then necessarily x < sup > 2 </ sup > = 2, yet no rational number has this property.

If the rational number's denominator has any prime factors other than 2 or 5, it cannot be expressed as a finite decimal fraction, and has a unique eventually repeating infinite decimal expansion.

The best known example is the ring of quaternions H. If we allow only rational instead of real coefficients in the constructions of the quaternions, we obtain another division ring.

* If f is an irreducible polynomial of prime degree p with rational coefficients and exactly two non-real roots, then the Galois group of f is the full symmetric group S < sub > p </ sub >.

If the suspect was under the influence of alcohol or drugs, or suffered from an emotional or mental condition that substantially impaired their capacity to make rational decisions, the courts may well decide that the suspect's waiver was not knowing and intelligent.

If human beings are rational animals of such-and-such a sort, then the moral virtues are ...( filling in the blanks is the difficult part ).

Rand summarizes: If chooses to live, a rational ethics will tell him what principles of action are required to implement his choice.

If every element of an ordered field lies between two elements of its rational subfield, then the field is said to be Archimedean.

If it were rational, it could be expressed as a fraction a / b in lowest terms, where a and b are integers, at least one of which is odd.

If the equation lacks a constant term a < sub > 0 </ sub >, then 0 is one of the rational roots of the equation.

If one uses a composite representation of an " overall " reaction, some may be rational fractions.

If all herders make this individually rational economic decision, the common will be depleted or even destroyed, to the detriment of all.

If we fail to justify simplicity considerations on the basis of the context in which we make use of them, we may have no non-circular justification: " just as the question ' why be rational?

If B has a smallest element among the rationals, the cut corresponds to that rational.

If the starting number is rational then this process exactly parallels the Euclidean algorithm.

) If formulated in von Neumann – Bernays – Gödel set theory, the surreal numbers are the largest possible ordered field ; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals ; it has also been shown that the maximal class hyperreal field is isomorphic to the maximal class surreal field.

If a chattel slave refuses to work, a number of punishments are also available ; from beatings to food deprivation – although economically rational slave owners practiced positive reinforcement to achieve best results and before losing their investment ( or even friendship ) by killing an expensive slave.

* If X is the Euclidean space, then the interior of the set of rational numbers is empty.

If offered a choice between 100 today or 100 in one year and there is a positive real interest rate throughout the year ceteris paribus, a rational person will choose 100 today.

If there is more than one possible equilibrium at any time then the more interesting implications of the theory of rational expectations do not apply.

* If d is a square free integer then the extension K = Q (√) is a quadratic field of rational numbers.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

If one integrates this picture, which corresponds to applying the fundamental theorem of calculus, one obtains Cavalieri's quadrature formula, the integral – see proof of Cavalieri's quadrature formula for details.

If such proof is established, Denmark will claim the North Pole.

If we insert vertices in random order, it turns out ( by a somewhat intricate proof ) that each insertion will flip, on average, only O ( 1 ) triangles – although sometimes it will flip many more.

:“ If an integer n is greater than 2, then has no solutions in non-zero integers a, b, and c. I have a truly marvelous proof of this proposition which this margin is too narrow to contain .”

If neither A nor B includes the idea of existence, then " some A are B " simply adjoins A to B. Conversely, if A or B do include the idea of existence in the way that " triangle " contains the idea " three angles equal to two right angles ", then " A exists " is automatically true, and we have an ontological proof of A's existence.

If some specific deductive system of first-order logic is sound and complete, then is it " perfect " ( a formula is provable iff it is a semantic consequence of the axioms ), thus equivalent to any other deductive system with the same quality ( any proof in one system can be converted into the other ).

If a statement P is provable, then it is certainly impossible to prove that there is no proof of P. But even if it can be shown that no disproof of P is possible, we cannot conclude from this absence that there is a proof of P. Thus P is a stronger statement than not-not-P.

If transitions do not exist, then there is no proof of any continuity between A and B.

If a set is well-ordered ( or even if it merely admits a wellfounded relation ), the proof technique of transfinite induction can be used to prove that a given statement is true for all elements of the set.

If, however, the subject lives a life of great extravagance, tell him he, too, can afford to give largely, the proof of his opulence being evident in his expenditure.

If proof emerges of the true extent of the state actor's involvement, this strategy can backfire ; for example see Iran-contra and Philip Agee.

If there was an intuitive element, it was to be isolated and represented separately as an axiom: from there on, the proof was to be purely logical and without gaps.

If V is a probabilisitic Turing Machine which could possible accept x if x is in X, then the proof is the string of coin flips which leads the machine, by luck, intuition, or genius, to accepting x.

If there is a real doubt, based upon reason and common sense after careful and impartial consideration of all the evidence, or lack of evidence, in a case, then the level of proof has not been met.

* Hardy once told Bertrand Russell " If I could prove by logic that you would die in five minutes, I should be sorry you were going to die, but my sorrow would be very much mitigated by pleasure in the proof ".

If this be a spirit of aggrandizement, the undersigned are prepared to admit, in that sense, its existence ; but they must deny that it affords the slightest proof of an intention not to respect the boundaries between them and European nations, or of a desire to encroach upon the territories of Great Britain.

If it did not, then the rum contained too much water and was considered to be " under proof ".

" Concerning the author, the critic said, " If ever on earth there lived a man who kept the law of Christ, and could give proof of it, and be absolutely unconscious that he was giving it to them, it is this man whom the Mongols called ' our Gilmour.

If we allow the elements of the system to use quantum computation, the system is called a quantum interactive proof system, and the corresponding complexity class is called QIP.

If the and are real numbers, a more elegant proof is available: the identity expresses the fact that the absolute value of the product of two quaternions is equal to the product of their absolute values, in the same way that the Brahmagupta – Fibonacci two-square identity does for complex numbers.

If a witness is reluctant to testify, then the personal service of subpoena is usually required with proof of service by non-party server.

If the three criteria above are met, the burden of proof shifts to the IRS and the IRS must prove that the compensation was unreasonable.