If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

If we assume that E ( t ) is made up of two colors at frequencies ω < sub > 1 </ sub > and ω < sub > 2 </ sub >, we can write E ( t ) as

If the pump waves are of frequency ω < sub > 1 </ sub >

If an object moves with angular velocity ω around a circle of radius r centered at the origin of the x-y plane, then its motion along each coordinate is simple harmonic motion with amplitude r and angular frequency ω.

If the Grover's search problem was solvable with log < sup > c </ sup > N applications of U < sub > ω </ sub >, that would imply that NP is contained in BQP, by transforming problems in NP into Grover-type search problems.

If there is a ΔA, then a small AC voltage will be present that corresponds to the modulation frequency, ω.

If an object ( particle ) is observed with frequency Ω >> ω in a half-space ( say, y < 0 ), then this observation prevents the particle, which stays in the half-space y > 0 from entry into this half-space y < 0.

If the flash occurs equal to the period of rotation ( or evenly multiplied or divided, i. e. n * ω or ω / n, where n is an integer and ω the angular frequency ) the marked point will appear to not move.

If j is the elementary embedding mentioned in one of these axioms and κ is its critical point, then λ is the limit of as n goes to ω.

# If K has no ω < sub > 1 </ sub >- Erdős cardinals, then for a particular countable ( in K ) and definable in K sequence of functions from ordinals to ordinals, every set of ordinals closed under these functions is a union of a countable number of sets in K. If L = K, these are simply the primitive recursive functions.

If these are ω < sub > 1 </ sub > and ω < sub > 2 </ sub > then all points not in the planes rotate through an angle between ω < sub > 1 </ sub > and ω < sub > 2 </ sub >.

If ω < sub > 1 </ sub > = ω < sub > 2 </ sub > the rotation is a double rotation and all points rotate through the same angle so any two orthogonal planes can be taken as the planes of rotation.

If one of ω < sub > 1 </ sub > and ω < sub > 2 </ sub > is zero, one plane is fixed and the rotation is simple.

If both ω < sub > 1 </ sub > and ω < sub > 2 </ sub > are zero the rotation is the identity rotation.

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.

Then I replied, coldly, `` If you despise me, why don't you say so, directly ''??

If Ferguson's car had been in sight, Holden would have walked directly to it.

If Hōkūleʻa could be kept directly overhead, they landed on the southeastern shores of the Big Island of Hawaiʻi.

If a party has gained more direct mandates in a Land than it is entitled to according to the results of the second vote, it does not forfeit these mandates because all directly elected candidates are guaranteed a seat in the Bundestag.

If there are any enemy discs on the board, a player must make contact, directly or indirectly, with an enemy disc during the shot.

If the corporate President is not the COO ( such as Richard Parsons of Time Warner from 1995 – 2001 ), then many division heads report directly to the CEO themselves, with the President taking on special assignments from the CEO.

If there is a tie, we must consider the atoms at distance 2 from the stereocenter — as a list is made for each group of the atoms bonded to the one directly attached to the stereocenter.

If the third layer is placed so that its atoms are directly above those of the first layer, the stacking will be ABA — this is the hcp structure, and it continues ABABABAB.

If the ball is carried by a player, it is considered a score when any part of the ball is directly above or beyond any part of the goal line between the pylons.

If water is evaporated too quickly, the membrane dries, resistance across it increases, and eventually it will crack, creating a gas " short circuit " where hydrogen and oxygen combine directly, generating heat that will damage the fuel cell.

If the node which has the requested file is not firewalled, the querying node can connect to it directly.

If the book itself, Animal Farm, had left any doubt of the matter, Orwell dispelled it in his essay Why I Write: ' Every line of serious work that I ’ ve written since 1936 has been written directly or indirectly against Totalitarianism ... dot, dot, dot, dot.

If this type of information is obtained ( directly or indirectly ) and there is reason to believe it is non-public, there is a duty to disclose it or abstain from trading.

If the former German and Ottoman territories had been ceded to the victorious powers directly, their economic value would have been credited to offset the Allies ' claims for war reparations.

If this image were transferred directly to paper, it would create a mirror-type image and the paper would become too wet.

If NAA is conducted directly on irradiated samples it is termed Instrumental Neutron Activation Analysis ( INAA ).

If the initial firing is above the surface of the Earth as shown, there will also be elliptical orbits at slower velocities ; these will come closest to the Earth at the point half an orbit beyond, and directly opposite, the firing point.

If the inverting input is held at ground ( 0 V ) directly or by a resistor, and the input voltage V < sub > in </ sub > applied to the non-inverting input is positive, the output will be maximum positive ; if V < sub > in </ sub > is negative, the output will be maximum negative.

" If anyone says that the blessed Apostle Peter was not established by the Lord Christ as the chief of all the apostles, and the visible head of the whole militant Church, or, that the same received great honour but did not receive from the same our Lord Jesus Christ directly and immediately the primacy in true and proper jurisdiction: let him be anathema.

Thus, personal involvement is linked with public opinion Proverbs that speak to the political disgruntlement include: “ When the Czar spits into the soup dish, it fairly bursts with pride ”; “ If the Czar be a rhymester, woe be to the poets ”; and “ The hen of the Czarina herself does not lay swan ’ s eggs .” While none of these proverbs state directly, “ I hate the Czar and detest my situation ” ( which would have been incredibly dangerous ), they do get their points across.

If the voters determine their preferences before the election and always vote directly consistent to them, they will emulate the Contingent vote and get the same results as if they were to use that system.

If the bell is placed on the patient, the vibrations of the skin directly produce acoustic pressure waves traveling up to the listener's ears.

If the male is an Abdi Dalem royal servant, courtier or particularly " peko-peko " ( taken directly from Japanese to mean obsequious ) or even a highly formal individual, he will retreat face and head downcast, never show his side or back to his superior, and retreat backwards in the following posture: left-arm crossed against the chest, right-arm hanging and walking stooped.

If in changing from one position to another the reflected image passes directly over the unreflected image, no side error exists.