If we try to choose an element from each set, then, because X is infinite, our choice procedure will never come to an end, and consequently, we will never be able to produce a choice function for all of X.

If a poet writes down several lines, intending them as a poem, the very procedure by which it is written makes it a poem.

If not, the curve is subdivided parametrically into two segments, 0 ≤ t ≤ 0. 5 and 0. 5 ≤ t ≤ 1, and the same procedure is applied recursively to each half.

If the earlier completion procedure is applied to a normed vector space, the result is a Banach space containing the original space as a dense subspace, and if it is applied to an inner product space, the result is a Hilbert space containing the original space as a dense subspace.

Given a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

If R is a Euclidean domain in which euclidean division is given algorithmically ( as is the case for instance when R = F where F is a field, or when R is the ring of Gaussian integers ), then greatest common divisors can be computed using a form of the Euclidean algorithm based on the division procedure.

If a subject after submitting to the hypnotic procedure shows no genuine increase in susceptibility to any suggestions whatever, there seems no point in calling him hypnotised, regardless of how fully and readily he may respond to suggestions of lid-closure and other superficial sleeping behaviour.

Clark L. Hull, probably the first major empirical researcher in the field, wrote If a subject after submitting to the hypnotic procedure shows no genuine increase in susceptibility to any suggestions whatever, there seems no point in calling him hypnotised ...

If it is not possible to fix the broken ligament, other procedures such as the Brunelli procedure can correct the instability.

If organic or inorganic contaminations are present on the wafer surface, they are usually removed by wet chemical treatment, e. g. the RCA clean procedure based on solutions containing hydrogen peroxide.

If the Council rules that the incapacity is permanent, the same procedure as for the resignation is applied, as described above.

If there is any evidence of this, methods of respiratory assistance must be on hand before and during the transfer procedure.

If a system identifies end-users by some form of log-in procedure then a concurrency goal is highly desirable.

If so, go to collision detected procedure.

If positive clones can be obtained from this procedure, the DNA is sequenced and PCR primers are chosen from sequences flanking such regions to determine a specific locus.

If the procedure is expected to result in significant blood loss, an autologous blood donation may be made some weeks prior to surgery.

If the surgery involves the digestive system, the patient may be instructed to perform a bowel prep by drinking a solution of polyethylene glycol the night before the procedure.

If their condition requires training, knowledge, surgical procedure, or equipment unavailable to the GP, the patient is then referred to a gynaecologist.

* Step 1: If h > 1 then first use this procedure to move the h-1 smaller disks from peg A to peg B.

* Step 3: If h > 1 then again use this procedure to move the h-1 smaller disks from peg B to peg C.

If the rules and logic of deduction are followed, this procedure ensures an accurate conclusion.

If the cause is gallstones, it is likely that an ERCP procedure or removal of your gallbladder will be recommended.

If dictionaries were logico-mathematical texts, then so-called circular definition would amount to infinite regress, where one of the steps involved in running the procedure is to run the procedure ; and, in the context of explanation ( as opposed to description in the form of dictionary definition ), this would be a vicious infinite regress.

If a town wishes to obtain the title of a city the proper method of procedure is to address a petition to the King through the Home Office.

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.