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Page "Complement (set theory)" ¶ 2
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If and universe
If the moral code were flouted, the proper balance of the universe would be upset, and the disastrous result could be floods, plague, or famine.
If this is true, then the universe today looks just as it did millions of years ago and as it will look millions of years hence, even though the universe is expanding.
If the universe is flat, there must be an additional component making up 73 % ( in addition to the 23 % dark matter and 4 % baryons ) of the energy density of the universe.
* If one refuses to sit down and make a move, one cannot be checkmated ( in relation to Russell's belief about the existence of the universe ).
If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made.
If confirmed, this would imply special relativity is an approximation to a more general theory, but since the relevant comparison would ( by definition ) be outside the observable universe, it is difficult to imagine ( much less construct ) experiments to test this hypothesis.
If this sounds indulgent, it allows simultaneity, absolute space and time and a deterministic universe ( along with decoherence theory ) whilst the status-quo permits time travel / causality paradoxes, subjectivity in the measurement process and multiple universes.
If the entire volume of the observable universe ( taken to be 3 × 10 < sup > 80 </ sup > m < sup > 3 </ sup >) were packed solid with fine dust particles about 1. 5 micrometres in size, then the number of different ways of ordering these particles ( that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered ) would be approximately one googolplex.
If the universe is static and populated by an infinite number of stars, any sight line from Earth must end at the ( very bright ) surface of a star, so the night sky should be completely bright.
If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell between 2, 000, 000, 000 to 2, 000, 000, 001 light years away.
If, on the other hand, the conception taken as the foundation of the system is that the great inclusive unity is the world itself, or the universe, God is swallowed up in that unity, which may be designated nature.
If one adds two whole parts the result is one whole and if one whole is subtracted from another whole the result is another whole-it means there is one whole universe and it is all prevaded by " Him ". Since the universe has come forth from the Divine, all things and beings are sacred and must be treated so in human thought and action.
If God in some sense knows ahead of time what will happen, then events in the universe are effectively predetermined from God's point of view.
If the energy density is positive, the associated negative pressure will drive an accelerated expansion of the universe, as observed.
If the universe is described by an effective local quantum field theory down to the Planck scale, then we would expect a cosmological constant of the order of.
If this type of energy were to exist, it would cause a big rip in the universe due to the growing energy density of dark energy which would cause the expansion of the universe to increase at a faster-than-exponential rate.
If there are as many monkeys as there are particles in the observable universe ( 10 < sup > 80 </ sup >), and each types 1, 000 keystrokes per second for 100 times the life of the universe ( 10 < sup > 20 </ sup > seconds ), the probability of the monkeys replicating even a short book is nearly zero.
If one assumes that all of the universe consists of protons and neutrons, the density of the universe is such that much of the currently observed deuterium would have been burned into helium-4.
If α were > 0. 1, stellar fusion would be impossible and no place in the universe would be warm enough for life as we know it.

If and U
If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.
If the United States were to punish a visiting diplomat without sufficient grounds, U. S. representatives in other countries could receive harsher treatment.
* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if is continuous and linear, then there exists an extension of φ which is also continuous and linear and which has the same norm as φ ( see Banach space for a discussion of the norm of a linear map ).
* If V is a normed vector space with linear subspace U ( not necessarily closed ) and if z is an element of V not in the closure of U, then there exists a continuous linear map with ψ ( x ) = 0 for all x in U, ψ ( z ) = 1, and || ψ || = 1 / dist ( z, U ).
If ƒ is complex differentiable at every point z < sub > 0 </ sub > in an open set U, we say that ƒ is holomorphic on U. We say that ƒ is holomorphic at the point z < sub > 0 </ sub > if it is holomorphic on some neighborhood of z < sub > 0 </ sub >.
Chinese immigrants were blamed for importing the opium-smoking habit to the U. S. The 1903 blue-ribbon citizens ' panel, the Committee on the Acquirement of the Drug Habit concluded, " If the Chinaman cannot get along without his dope we can get along without him.
“ The U. S. Fish and Wildlife Service-funded Ivory-billed Woodpecker searches will continue through the 2008-09 search season ,” says Laurie Fenwood, Ivory-billed Woodpecker Recovery Team Coordinator for the U. S, Fish and Wildlife Service .… If no birds are confirmed, the Cornell Lab of Ornithology will not send an organized team into the field next year.
If I manage to leave for the U. S., then I will be over there.
If a judge determines that there is sufficient evidence to believe that the defendant committed the crime, it is said that the defendant is " held to answer " or " bound over " ( in U. S. jurisdictions ).
If rotations are also considered distinct, then the pentominoes from the first category count eightfold, the ones from the next three categories ( T, U, V, W, Z ) count fourfold, I counts twice, and X counts only once.
If one considers a version of QCD with N < sub > f </ sub > flavors of massless quarks, then there is a global ( chiral ) flavor symmetry group SU < sub > L </ sub >( N < sub > f </ sub >) × SU < sub > R </ sub >( N < sub > f </ sub >) × U < sub > B </ sub >( 1 ) × U < sub > A </ sub >( 1 ).
If an electron of energy E is incident upon an energy barrier of height U ( z ), the electron wave function is a traveling wave solution,
If the bias is small, we can let U − E ≈ φM in the expression for κ, where φM, the work function, gives the minimum energy needed to bring an electron from an occupied level, the highest of which is at the Fermi level ( for metals at T = 0 kelvins ), to vacuum level.
If U. S. officials can " help clean up his image " and lift the ban on arms sales to the Panamanian Defense Force, Noriega will "' take care of ' the Sandinista leadership for us.
But they soon had another US No. 2 hit with a cover of Simon & Garfunkel's " A Hazy Shade of Winter " from the soundtrack of the film Less Than Zero, and the melancholic " If She Knew What She Wants ", written by Jules Shear, reached the U. S. Top 30 and the German Top 20.
The U. S. Supreme Court explained this, in U. S. Public Workers v. Mitchell: " If granted power is found, necessarily the objection of invasion of those rights, reserved by the Ninth and Tenth Amendments, must fail.

If and is
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.

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