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 you were a man '' --

If she, Pamela, were being held responsible for his crimes, then hers must be the final act of expiation.

If someone were to drop a match in here, this place would go up like a haystack ''.

If the other pilots were worried, they did not show it.

If it were the enemy, tactically his position was correct.

If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;

If it were not that I knew who it was I could have mistaken it for my Aunt so well did her clothes fit him.

If an automobile were approaching him, he would know what was required of him, even though he might not be able to act quickly enough.

If there were only darkness, all would be clear.

If there were only the mess, all would be clear ; ;

If these people were denied a voice ( do they have a moral right to a voice??

If we were creating a wholly new society, we could insist that our social, political, economic and philosophic institutions foster rather than hamper man ; ;

If living Jews were unavailable for study, the Bible was at hand.

If his scholarship and formal musicianship were not all they might have been, Mercer demonstrated at an early age that he was gifted with a remarkable ear for rhythm and dialect.

If she were not at home, Mama would see to it that a fresh white rose was there.

If the Stearns were not there, grace would be omitted.

If anything, the conservative Democrats were more opposed to Hearst than the Republicans.

If the hardships of the winter at Valley Forge were trying for healthy men, they were, of course, much more so for those not in good health.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If there were no West Berlin problem, imperialist quarters would have invented an excuse for stepping up the armaments race to try to solve the internal and external problems besetting the United States and its NATO partners.

If the new Soviet series has followed the general pattern of previous Russian tests, the shots were roughly half fission and half fusion, meaning a fission yield of 30 to 40 megatons thus far.

If the Hessian troops sent here willy-nilly by the Hessian Government to fight for England in the 1770's were mercenaries, what shall we call the UN troops sent to the Congo willy-nilly by their governments to fight for the United Nations??

If the UN troops are not mercenaries then the Hessians were not mercenaries either.

If he were to go with White, he would be out there two days, not just listening in the dark at some point between here and Papa-san, but moving ever deeper into enemy land -- behind Papa-san -- itself.