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 companies will take the time to give objective consideration to their major problems and to the questions they provoke, then a long constructive step will have been taken toward more effective marketing in next decade.

# If morality is objective and absolute, God must exist.

But this destruction, coupled with a protracted siege of Rain ( 9 – 16 July ), caused Prince Eugene to lament "... since the Donauwörth action I cannot admire their performances ", and later to conclude " If he has to go home without having achieved his objective, he will certainly be ruined.

If wave function collapse is regarded as ontologically real as well, an objective collapse theory is obtained.

If anything, if a part of objective reality, theorization and systemization to Post-structuralists was an exponent of larger, more nebulous patterns of control in social orders – patterns that could not be encapsulated in theory without simultaneously conditioning it.

If the main objective of a campaign was not the conquest of a particular city, it could simply be passed by.

If Viola's depictions of emotional states with no objective correlative -- emotional states for which the viewer has no external object or event to understand them by — are one feature of many of his works, another, which has come to the forefront, is his reference to medieval and classical depictions of emotion.

If the objective is to raise as much money as possible for the issuer, a traditional IPO, priced near the top end of the underwriter's range, would likely achieve that objective.

If there are alternative ways of solving a problem, we do not sit to determine which of them is best suited to achieve a valid state objective.

If the objective is NOT attainable a different objective must be selected and the process repeated.

If the distance between the beam steering lenses and the objective are chosen properly, this will correspond to a similar deflection before entering the objective and a resulting lateral translation in the sample plane.

If the Office links to a Depot that has a link to a friendly town, the Depot is referred to as " Spawnable " and players may spawn from new missions there, making them an important objective.

If it is assumed that the residuals belong to a Normal distribution, the objective function, being a sum of weighted squared residuals, will belong to a Chi-squared () distribution with m-n degrees of freedom.

# If the objective of the SAA problem converges to the true problem's objective with probability 1, as, uniformly on the feasible set.

If the player fails to complete the secondary objective on the first attempt, they can revisit the mission later.

If there is no special style indicated by the server owner, the only objective is the above ( to simply kill opponent tanks ); it is called a " free for all ", or " FFA " for short.

If the objective of the quest has not been accomplished then the evil wizard character wins.

If the objective function is concave ( maximization problem ), or convex ( minimization problem ) and the constraint set is convex, then the program is called convex and general methods from convex optimization can be used in most cases.

If the objective function is a ratio of a concave and a convex function ( in the maximization case ) and the constraints are convex, then the problem can be transformed to a convex optimization problem using fractional programming techniques.

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 a union cannot perform this function, then collective bargaining is being palmed off by organizers as a gigantic fraud.

If the Greek letter is used, it is assumed to be a Fourier transform of another function,

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 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 the function R is well-defined, its value must lie in the range, with 1 indicating perfect correlation and − 1 indicating perfect anti-correlation.

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

If f is not a function, but is instead a partial function, it is called a partial operation.

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as ( a ) your void is useful ( i. e., does not duplicate the function of an ace that your side holds ) and ( b ) you are not vulnerable to the loss of the first two tricks in the fourth suit ( because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control ).

If evolutionary processes are blind to the difference between function F being performed by conscious organism O and non-conscious organism O *, it is unclear what adaptive advantage consciousness could provide.

If the wave function is regarded as ontologically real, and collapse is entirely rejected, a many worlds theory results.

If we take the simple valence bond structure and mix in all possible covalent and ionic structures arising from a particular set of atomic orbitals, we reach what is called the full configuration interaction wave function.

If we take the simple molecular orbital description of the ground state and combine that function with the functions describing all possible excited states using unoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configuration interaction wavefunction.

If f is also surjective and therefore bijective ( since f is already defined to be injective ), then S is called countably infinite.

If we attempt to use the above formula to compute the derivative of f at zero, then we must evaluate 1 / g ′( f ( 0 )).

If k, m, and n are 1, so that and, then the Jacobian matrices of f and g are.

If f is a function of as above, then the second derivative of is:

If we let f be a function

If a probability distribution has a density function f ( x ), then the mean is

If the function f is not linear ( i. e. its graph is not a straight line ), however, then the change in y divided by the change in x varies: differentiation is a method to find an exact value for this rate of change at any given value of x.

If the limit exists, then f is differentiable at a.

If f is a continuous function, meaning that its graph is an unbroken curve with no gaps, then Q is a continuous function away from.

If the limit exists, meaning that there is a way of choosing a value for Q ( 0 ) that makes the graph of Q a continuous function, then the function f is differentiable at a, and its derivative at a equals Q ( 0 ).

If y = f ( x ) is differentiable at a, then f must also be continuous at a.

If in the third identity we take H = G, we get that the set of commutators is stable under any endomorphism of G. This is in fact a generalization of the second identity, since we can take f to be the conjugation automorphism.

If f is a surjection and a ~ b ↔ f ( a ) = f ( b ), then g is a bijection.

If m and n are natural numbers and f ( x ) is a smooth ( meaning: sufficiently often differentiable ) function defined for all real numbers x in the interval, then the integral