If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

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 an evacuated glass tube is equipped with two electrodes and a voltage is applied, the glass opposite of the negative electrode is observed to glow, due to electrons emitted from and travelling perpendicular to the cathode ( the electrode connected to the negative terminal of the voltage supply ).

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.

If the disc cannot be found, there must be " reasonable evidence " that the disc went out-of bounds or the lost disc penalty is applied.

If ultra-pure products are the goal, then further chemical separation must be applied.

To avoid debates about the possibility of in-vitro fertilization, artificial insemination, or cloning, the original Darwin Awards book applied the following " deserted island " test to potential winners: If the person were unable to reproduce when stranded on a deserted island with a fertile member of the opposite sex, he or she would be considered sterile.

If a function that is not injective is applied to both sides of a true equation, then the resulting equation will still be true, but it may be less useful.

If a chemical reaction is driven by an external applied voltage, as in electrolysis, or if a voltage is created by a chemical reaction as in a battery, it is an electrochemical reaction.

If applied to optical wavelengths, this manifests itself as a change in the colour of visible light as the wavelength of the light is increased toward the red part of the light spectrum.

If the magnetic field is applied by a solenoid, the sensor output is proportional to the product of the current through the solenoid and the sensor voltage.

If the rule is interpreted as defining an inertial frame, then we have to be able to determine when zero net force is applied.

If the applied pump power is too small, the gain will never be sufficient to overcome the resonator losses, and laser light will not be produced.

If an electric field of one particular polarity is applied for a long period of time, this ionic material is attracted to the surfaces and degrades the device performance.

If a force is applied to a particle for a time interval, the momentum of the particle changes by an amount

If a and b are distances from the fulcrum to points A and B and if force F < sub > A </ sub > applied to A is the input force and F < sub > B </ sub > exerted at B is the output, the ratio of the velocities of points A and B is given by a / b, so the ratio of the output force to the input force, or mechanical advantage, is given by

If the inverting input is held at ground ( 0 V ) directly or by a resistor, and the input voltage V < sub > in </ sub > applied to the non-inverting input is positive, the output will be maximum positive ; if V < sub > in </ sub > is negative, the output will be maximum negative.

If the voltage to be sensed, E < sub > i </ sub >, is applied to op amp's (+) input, the result is a noninverting positive-level detector: when E < sub > i </ sub > is above V < sub > ref </ sub >, V < sub > O </ sub > equals + V < sub > sat </ sub >; when E < sub > i </ sub > is below V < sub > ref </ sub >, V < sub > O </ sub > equals − V < sub > sat </ sub >.

If E < sub > i </ sub > is applied to the inverting input, the circuit is an inverting positive-level detector: When E < sub > i </ sub > is above V < sub > ref </ sub >, V < sub > O </ sub > equals − V < sub > sat </ sub >.

If the revenue the firm is receiving is greater than its total variable cost ( R > VC ) then the firm is covering all variable cost plus there is additional revenue (" contribution "), which can be applied to fixed costs.

If the same concept is correctly and non-arbitrarily applied to two individuals, there must be some resemblance or shared property between the two individuals that justifies their falling under the same concept and that is just the metaphysical problem that universals were brought in to address, the starting-point of the whole problem ( MacLeod & Rubenstein, 2006, § 3d ).

If the negated query can be refuted, i. e., an instantiation for all free variables is found that makes the union of clauses and the singleton set consisting of the negated query false, it follows that the original query, with the found instantiation applied, is a logical consequence of the program.

If an unmarried couple change residence to different countries, then the local law on where the couple is last domiciled is applied to them.

If the data to be compressed is analog ( such as a voltage that varies with time ),

If drain-to-source voltage is increased, this creates a significant asymmetrical change in the shape of the channel due to a gradient of voltage potential from source to drain.

If drain-to-source voltage is increased further, the pinch-off point of the channel begins to move away from the drain towards the source.

If the answer was incorrect, the teacher would administer a shock to the learner, with the voltage increasing in 15-volt increments for each wrong answer.

If the voltage changes by a large enough amount, an all-or-none electrochemical pulse called an action potential is generated, which travels rapidly along the cell's axon, and activates synaptic connections with other cells when it arrives.

If predictable operation is desired, negative feedback is used, by applying a portion of the output voltage to the inverting input.

If the input voltages change in the same direction, the negative feedback makes Q3 / Q4 base voltage follow ( with 2V < sub > BE </ sub > below ) the input voltage variations.

If the base current to the transistor is assumed to be zero, the negative feedback forces the transistor to increase its collector-emitter voltage up to 1 V until its base-emitter voltage reaches 0. 625 V ( a typical value for a BJT in the active region ).

If the component is a resistor with time-invariant voltage to current ratio, then:

If the voltage is zero, this means that the resistance is zero.

If the collector voltage were zero, the collector current would be limited only by the light bulb resistance and the supply voltage.

If a load is connected to the secondary winding, the load current and voltage will be in the directions indicated, given the primary current and voltage in the directions indicated ( each will be alternating current in practice ).

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.