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 the applied voltage is large enough, the liquid crystal molecules in the center of the layer are almost completely untwisted and the polarization of the incident light is not rotated as it passes through the liquid crystal layer.

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 enough electricity is provided by solar panels, wind turbines, or other means, then electric heaters and stoves become a practical autonomous design.

If enough electric power is available, cooling can be provided by conventional air conditioning using a heat pump.

where Q is the electric charge transferred through the surface over a time t. If Q and t are measured in coulombs and seconds respectively, I is in amperes.

If only the electric field () is non-zero, and is constant in time, the field is said to be an electrostatic field.

If used in a permanent installation, a split sensor allows the electric current to be tested without dismantling the existing circuit.

If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

If they did exist, both Gauss's law for magnetism and Faraday's law would need to be modified, and the resulting four equations would be fully symmetric under the interchange of electric and magnetic fields ; see magnetic monopoles for details.

If plasma is pushed hard enough, it generates electric fields which allow it to move in response to the push, often ( not always ) deforming the magnetic field in the process.

If the user opens the protective sliding door that covers the pins, the processor can be exposed to any electric charge the user has built up.

If the dipole moment can be reversed by the application of an electric field, the material is said to be ferroelectric.

If the sunspot were isolated from the surrounding photosphere it would be brighter than an electric arc.

If the appliance is one whose purpose is for light or heat ( such as an incandescent lightbulb or electric oven ) then the lighting or heating elements may be considered as a type of fire ; if so, then turning them on constitutes both " lighting a fire " ( category 37 ) and " cooking " ( a form of baking, category 11 ), and turning them off would be " extinguishing a fire " ( category 36 ).

If this condition is met, the input electric power must equal the output power:

If the components of the computer were too large or the wires interconnecting them too long, the electric signals couldn't travel fast enough through the circuit, thus making the computer too slow to be effective.

If an electric boat has sails as well, and will be used in deep water ( deeper than about 15 m or 50 ft ), then a towed generator can help build up battery charge while sailing ( there is no point in trailing such a generator while under electric propulsion as the extra drag from the generator would waste more electricity than it generates ).

If the wave is frozen in time, the electric field vector of the wave describes a helix along the direction of propagation.

If more than one charge is present, the total electric field at any point is equal to the vector sum of the separate electric fields that each point charge would create in the absence of the others.

If several spatially distributed charges generate such an electric potential, e. g. in a solid, an electric field gradient may also be defined.

If this susceptibility itself depends upon the electric field, one can obtain a nonlinear optical effect of magneto-optical parametric generation ( somewhat analogous to a Pockels effect whose strength is controlled by the applied magnetic field ).

If one considers the flux of the electric field vector, E, for a tube near a point charge in the field the charge but not containing it with sides formed by lines tangent to the field, the flux for the sides is zero and there is an equal and opposite flux at both ends of the tube.