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 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 the pitch of this twist is on the order of the wavelength of visible light, then interesting optical interference effects can be observed.

If we now subject the atoms to light of a frequency, the process of optical absorption will excite the atoms from the ground state to level 3.

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 instead it refers to the signal power incident on the detector system, it is called the optical NEP.

If a photographic plate or another 2-D optical sensor is located within the scattered light field without a lens, a speckle pattern is obtained whose characteristics depend on the geometry of the system and the wavelength of the laser.

If absorption of light varies with the angle relative to the optical axis in a crystal then pleochroism results.

If the curvature of a surface of a lens is C and the index of refraction is n, the optical power is φ = ( n − 1 ) C. If both surfaces of the lens are curved, consider their curvatures as positive toward the lens and add them.

If it is decided to produce fringes in white light, then, since white light has a limited coherence length, on the order of microns, great care must be taken to equalize the optical paths or no fringes will be visible.

If we consider a transparent cube of length on a side, filled with soot, then the optical depth of this medium is inversely proportional to the square of, and therefore proportional to the areal density of soot particles: we can make it easier to see through the imaginary cube just by making the cube larger.

If one end of the optical fiber is moulded into a lens-like facet, the nearly gaussian beam carried by a single mode standard fiber will be focussed at some distance from the fiber tip.

If light of a fixed frequency / wavelength / color ( as from a laser ) is assumed, then the time-harmonic ( frequency-domain ) form of the optical field is given as:

If the emitted light is of a specific visible wavelength it may be called colorimetry, or it may involve specific wavelength of light e. g. by use of laser and emission of fluorescent signals of another specific wavelength which is detected via very specific wavelength optical filters.

If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances.

If an optical system is not axisymmetric, either due to an error in the shape of the optical surfaces or due to misalignment of the components, astigmatism can occur even for on-axis object points.

If visual loss is significant, surgical removal of the lens may be warranted, with lost optical power usually replaced with a plastic intraocular lens ( IOL ).

If the optical filter passed only that frequency band, then there would be a net transfer of photons, and their energy, from the second system to the first.

If the optical cavity is not empty ( e. g., a laser cavity which contains the gain medium ), the value of L used is not the physical mirror separation, but the optical path length between the mirrors.

If there are not many fiber optic cables to the node, wavelength division multiplexing can be utilised to combine multiple optical signals onto the same fiber.

If the slope is gentle, then optical fiber has a satisfactory loss characteristic.

If an optical fiber experiences mechanical strain, the dimensions of the fiber will be altered, thus resulting in a change in the resonant wavelength of light emitted.

If we position ourselves so that the screen is directly between ourselves and the optical device ( mirror, lens, etc.