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 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 the Dominican Republic achieves free, democratic government, it will be due in large part to the U.S. show of force that enabled President Balaguer to prevent a threatened restoration of Trujillo dictatorship.

If a vaulter achieves a miss on their first attempt at a height, they can pass to the next height, but they will only have two attempts at that height, as they will be out once they achieve three consecutive misses.

If the theory of quantum gravity also achieves a grand unification of the other known interactions, it is referred to as a theory of everything ( TOE ).

If a bottle neck communication link offering data rate R is shared by " N " active users ( with at least one data packet in queue ), every user typically achieves a throughput of approximately R / N, if fair queuing best-effort communication is assumed.

If the system has some other mechanism for per-process address spaces, such as a segment register, copying the entire process memory to the new process achieves the desired effect, however this is a costly operation and most likely unneeded given that the new process almost immediately replaces the process image in most instances.

If on the count of primary or first preference votes ( votes marked with the number ' 1 '), no candidate achieves more than 50 % of the vote, the candidate with the fewest votes is excluded and their votes distributed according to the next available preferences, their 2nd or third choice candidate.

If the player achieves a Major Victory both in Britain and in Moscow, he or she is allowed to invade Washington.

If the target diameters of the two clusters are known, a clustering that achieves those targets may be found by solving a 2-satisfiability instance.

If the company achieves predetermined sales, earnings or profitability goals, the investors receive an additional dividend.

If he achieves both milestones, he will be the first man in Venezuelan baseball history to reach both marks.

If the substrings in question are long, this algorithm achieves great savings compared with many other hashing schemes.

If he achieves this first, he will be readmitted to Heaven.

If we can solve for then we can find from it a control that achieves the minimum cost.

If a Marine achieves the qualification of expert multiple times consecutively, an additional " rung " is added to the appropriate badge denoting the number of consecutive awards.

* Decision: If neither wrestler achieves either a fall or technical superiority, the wrestler who scored more points during the period is declared the winner of that period.

If Selene only drains the victim's life force partially, she achieves a measure of psychic control over her victim's mind, thereby subverting them to her will.

If this orb is destroyed in a chain, the player achieves Fever status for the next several seconds.

If he is not found, he achieves freedom on his own and successfully sponsors a bill where all mutants are sent to re-education camps where they will be brutally educated to not use their powers.

If Team Jack's Mannequin achieves this goal, they will have raised half a million dollars for the Light the Night Walk.

If the thesis grade is an A ( 94 %) or A-( 90 %), then the student achieves honors in major and receives an honorable mention in the annual university awards ceremony.