If the photographically realistic continuity of dreams, however bizarre their combinations, denies that it is purely a composition of the brain, it must be compounded from views of diverse realities, although some of them may never be encountered in what we are pleased to call the real life.

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

* In an issue of the What If series, Cannonball's brother Josh ( who would, in normal continuity, later become Icarus ) found and " adopted " a Sentinel.

If one does not require a ring to have a unit, then one has to add the requirement of continuity of the additive inverse, or equivalently, to define the topological ring as a ring which is a topological group ( for +) in which multiplication is continuous, too.

If something happened outside current continuity ( such as the so-called " Imaginary Stories " that were a staple of DC's Silver Age publications ), it was explained away as happening on a parallel world, a premise not dissimilar to the company's current Elseworlds imprint.

DC in particular periodically revisits the idea in major crossover storylines, such as Crisis on Infinite Earths and Infinite Crisis, where Marvel has a series called What If ... that's devoted to exploring alternative realities, which sometimes impact the " main " universe's continuity.

If recanalization proceeds it provides capillary-sized channels through the thrombus for continuity of blood flow through the entire thrombus but may not restore sufficient blood flow for the metabolic needs of the downstream tissue.

If the disturbance is not too large, the various physical quantities associated with the perturbed system ( e. g. its energy levels and eigenstates ) can, from considerations of continuity, be expressed as ' corrections ' to those of the simple system.

If f and g are germ equivalent at x, then they share all local properties, such as continuity, differentiability etc., so it makes sense to talk about a differentiable or analytic germ, etc.

Unlike its Marvel Comics counterpart What If ...?, which bases its stories on a single point of divergence from the regular continuity, most Elseworlds stories instead take place in entirely self-contained continuities, with the only connection to the canon DC continuity being the presence of familiar DC characters.

If Berossos believed in the continuity of history with patterns that repeated themselves ( i. e., cycles of events as there were cycles of the stars and planets ), a bare narrative would suffice.

If and has modulus of continuity,

* If has as modulus of continuity and, then, obviously, admits too as modulus of continuity.

* If and are functions between metric spaces with moduli respectively and, then the composition map has modulus of continuity.

* If and are functions from the metric space X to the Banach space, with moduli respectively and, then any linear combination has modulus of continuity.

* If and are bounded real-valued functions on the metric space, with moduli respectively and, then the pointwise product has modulus of continuity.

* If is a family of real-valued functions on the metric space with common modulus of continuity, then the inferior envelope, respectively, the superior envelope, is a real-valued function with modulus of continuity, provided it is finite valued at every point.

If the pericycle is superficial and the cortex is retained either the endodermis is stretched or crushed or it keeps pace with the expansion of the vascular cylinder by radial anticlinal divisions, the new walls developing Casparian strips in continuity with the old ones.

Thus, boundedness of T < sup >∗</ sup > on its domain does not imply boundedness of T. On the other hand, if T < sup >∗</ sup > is defined on the whole space then T is bounded on its domain and therefore can be extended by continuity to a bounded operator on the whole space .< ref > Proof: being closed, the everywhere defined T < sup >∗</ sup > is bounded, which implies boundedness of T < sup >∗∗</ sup >, the latter being the closure of T. See also for the case of everywhere defined T .</ ref > If the domain of T < sup >∗</ sup > is dense, then it has its adjoint T < sup >∗∗</ sup >.

If this was indeed Grant, it may indicate that as far as the Big Finish continuity is concerned, he was written out of history.

If that was Sam, it may indicate that, as far as the Big Finish continuity is concerned, she was written out of history.

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, in the trustee's judgment, `` reasonable market conditions '' did not prevail during any given year, he was to be allowed to petition the court for an extension of time within the ten-year period.

If it is assumed that the formula given by Lodge of cosec Af applies, the pressure difference along the major axes can be calculated from the angle of inclination of the major axis, and from this the interfacial tension can be calculated.

If one assumes that the average flux did not change between measurements, a mass-distribution curve is obtained which relates the flux of particles larger than a given radius to the inverse 7/2 power of the radius.

If, however, we are seeking the optimal R-stage policy for a given feed state, only one search for a maximum is required at the final step.

If the latter knows nothing about the absent sitter except his name ( given by the experimenter ), he cannot possibly give any clues, conscious or unconscious, far less ask leading questions.

`` If you substitute ' atom ' for ' angel ', the problem is not insoluble, given the metallic content of the pin in question ''.

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.

** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

( If the condition is thought to be cellulitis rather than abscess, consideration should be given to possibility of strep species as cause that are still sensitive to traditional anti-staphylococcus agents such as dicloxacillin or cephalexin in patients able to tolerate penicillin ).

If we use a cylindrical coordinate system with basis vectors, then the gradient of and the divergence of are given by

If the resulting four kilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256-entry 32-bit ( i. e. 1 kilobyte ) table by the use of circular rotates.

* If the balance factor of P is-2 then the right subtree outweighs the left subtree of the given node, and the balance factor of the right child ( R ) must be checked.

* If the balance factor of P is 2, then the left subtree outweighs the right subtree of the given node, and the balance factor of the left child ( L ) must be checked.

If the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.

If two equivalent amplifiers are being compared, the amplifier with higher gain settings would be more sensitive as it would take less input signal to produce a given amount of power.

If the norm of a Banach space satisfies this identity, the associated inner product which makes it into a Hilbert space is given by the polarization identity.

If BCG is accidentally given subcutaneously, then a local abscess may form ( a BCG-oma ) that can sometimes ulcerate, and may require treatment with antibiotics.

If given subcutaneously, it may induce local infection and spread to the regional lymph nodes, causing either suppurative and nonsuppurative lymphadenitis.

If BCG is accidentally given to an immunocompromised patient ( e. g., an infant with SCID ), it can cause disseminated or life-threatening infection.

If players cannot move either die in a roll, given the position of their checkers then that turn is over and the turn passes to the opponent.

If a source emits a known luminous intensity I < sub > v </ sub > ( in candelas ) in a well-defined cone, the total luminous flux Φ < sub > v </ sub > in lumens is given by

He explained that this is one of the most important analects: " If the people be led by laws, and uniformity sought to be given them by punishments, they will try to avoid the punishment, but have no sense of shame.

If they be led by virtue, and uniformity sought to be given them by the rules of propriety, they will have the sense of the shame, and moreover will become good.

* If the metric space X is compact and an open cover of X is given, then there exists a number such that every subset of X of diameter < δ is contained in some member of the cover.