If an atom bomb in 1945 could destroy an entire city surely the atomic arsenal we now have is more than adequate to fulfill any military objective required of it.

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 a system is composed of two subsystems described in V and W respectively, then the Hilbert space of the entire system is the tensor product of the two spaces.

If x is held fixed, then the Bessel functions are entire functions of α.

If there is still a tie, each atom in each of the two lists is replaced with a sub-list of the other atoms bonded to it ( at distance 3 from the stereocenter ), the sub-lists are arranged in decreasing order of atomic number, and the entire structure is again compared atom by atom.

If the operating system's memory is corrupted, the entire computer system may crash and need to be rebooted.

* If the entire language does not allow side-effects, then any evaluation strategy can be used ; this gives the compiler freedom to reorder or combine the evaluation of expressions in a program ( for example, using deforestation ).

If a compression scheme is lossless — that is, you can always recover the entire original message by uncompressing — then a compressed message has the same quantity of information as the original, but communicated in fewer bits.

If entire segments of the population are excluded from a sample, then there are no adjustments that can produce estimates that are representative of the entire population.

If the input has no syntax errors, the parser continues with these steps until all of the input has been consumed and all of the parse trees have been reduced to a single tree representing an entire legal input.

If he succeeded and built the Holy Temple in its proper place and gathered the dispersed ones of Israel together, this is indeed the anointed one for certain, and he will mend the entire world to worship the Lord together, as it is stated: " For then I shall turn for the nations a clear tongue, so that they will all procalim the Name of the Lord, and to worship Him with a united resolve ( Zephaniah 3: 9 ).

If the bark is removed around the entire circumference of a tree it is likely to die.

If the family was too small to finish eating the entire offering in one sitting, an offering was made for a group of families.

If he used the same practice in Norway, Thule is at least the entire northwest coast of Norway from Trondheim to the Lofoten Islands.

Physicalism is then further divided depending on whether it can be known a priori or a posteriori that: If physicalism is true, S is the statement that describes the entire physical nature of the world collectively, and S * is the statement that describes the entire nature of the world, then S entails S *.

If the idea of absolute freedom and entire self-knowledge is absent from this kind of idea of God's acts in time, then God Himself is ( to express the idea anthropomorphically ) becoming something new, or discovering something new about Himself with each new moment, just as we are.

If the Supreme Court finds any referred part unconstitutional, the entire bill falls.

If the mutation rate is too high, exceeding what is known as the error threshold, the quasispecies will break down and be dispersed over the entire range of available sequences.

If the producers chose to reformat the entire show for the 16: 9 ratio, live-action footage would have to be recropped, widening the frame to the full width of the 35 mm negatives while reducing its height.

If successful, this is followed by a service of Glorification in which the Saint is given a day on the church calendar to be celebrated by the entire church.

If a traffic accident occurs on a collector road, or if road construction inhibits the flow, then the entire road system may be rendered useless until the blockage is cleared.

* If θ > θ < sub > c </ sub >, the entire ray reflects from the boundary.

If the volume is the molal volume, then Af is obtained on a molal basis which is the customary terminology of the chemists.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

If the retailer and hotelman's downtown unit sales have been decreasing, however, his dollar volume continues to rise, and it is dollars which you put in the bank.

If we take in our hand any volume ; of divinity or school metaphysics, for instance ; let us ask, Does it contain any abstract reasoning concerning quantity or number?

* Continuity: If a certain mass of fluid enters a volume, it must either exit the volume or change the mass inside the volume.

If the boat floats, the mass of the boat ( plus contents ) as a whole divided by the volume below the waterline is equal to the density of water ( 1 kg / l ).

If weight is added to the boat, the volume below the waterline will increase to keep the weight balance equal, and so the boat sinks a little to compensate.

If the occulting object has an atmosphere, however, some of the luminosity of the star can be refracted into the volume of the umbra.

If we choose the shape of the control volume such that all flow in or out occurs perpendicular to its surface, then the flow of matter into the system performs work as if it were a piston of fluid pushing mass into the system, and the system performs work on the flow of matter out as if it were driving a piston of fluid.

If, however, the cylinders are at some angle to one another, then there is a large volume surrounding the cylinder which the approaching cylinder's center-of-mass cannot enter ( due to the hard-rod repulsion between the two idealized objects ).

If both sides of this equation are divided by the volume of this small piece of the charge distribution dV, the result is:

If momentum is to be conserved in a volume, changes in the momentum of matter through the Lorentz force must be balanced by changes in the momentum of the electromagnetic field and outflow of momentum.

If is the momentum of all the particles in a volume, and the particles are treated as a continuum, then Newton's second law gives

If brewers decide to convert their brew to a non-alcoholic brew they must consider the volume of liquid they have lost from the removal of the alcohol.

If the liquid is heated a little over 100 ° C, the transition from liquid to gas will occur not only at the surface, but throughout the liquid volume: the water boils.

If the areas of the two parallel faces are A < sub > 1 </ sub > and A < sub > 3 </ sub >, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A < sub > 2 </ sub >, and the height ( the distance between the two parallel faces ) is h, then the volume of the prismatoid is given by ( This formula follows immediately by integrating the area parallel to the two planes of vertices by Simpson's rule, since that rule is exact for integration of polynomials of degree up to 3, and in this case the area is at most a quadratic in the height.

If the field is increased past the optimum, further volume reductions are possible with minimal increase in cost.

If it is used for its relation between pressure and volume and temperature, a thermometric material must have three properties:

If a sound absorbing sheet is slid in between the prongs of a vibrating fork, reducing the waves reaching the ear from one prong, the volume heard will actually increase, due to a reduction of this cancellation.

If the liquid is incompressible the molar volume is constant and the integral becomes.

If an industry is characterized by a varying demand ( that is, a demand with cyclical fluctuations ), it is more difficult for the firms in the cartel to detect whether any change in their sales volume is due to a demand fluctuation or to cheating by another member of the cartel.