We suppose not.

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

We may reasonably suppose, that, when he rose to notice, he did not want the counsels and admonitions of scholars and critics, and that he at last deliberately persisted in a practice, which he might have begun by chance.

We might suppose we have a better conception of what minds are, because we are all ( the private language argument notwithstanding ) intimately acquainted with our own minds.

After their Defeat the Rebels retired to the Isle aux Noix, where they continued till lately, sending out some Parties, and many Emissaries, to debauch the Minds of the Canadians and Indians, in which they have proved too successful, and for which they were too well prepared by the Cabals and Intrigues of these two last years ; We knew of their being reinforced, and very considerably, I suppose, as they appeared in Numbers near St. John's last Sunday Evening ; where or when they landed, or the Particulars since, we have but very imperfect Accounts of, all Communications with the Forts of St. John's and Chambli, being, as far as I can find, entirely cut off.

We were all three, I suppose.

We suppose that, from one time step to the next, and intersect, then it is very likely that at the next time step, they will still intersect.

We will suppose that the put and call options are on traded stocks, but the underlying can be any other tradeable asset.

Regarding the scrolls De Vaux cautiously stated that " manuscripts were copied in the scriptorium of Qumran ... We may also suppose ... that certain works were composed at Khirbet Qumran.

We can use this fact to prove part of a famous result: for any prime p such that p ≡ 1 ( mod 4 ) the number (− 1 ) is a square ( quadratic residue ) mod p. For suppose p = 4k + 1 for some integer k. Then we can take m = 2k above, and we conclude that

We suppose that ; otherwise it is obvious that is a divergent series.

We may suppose ', but perturbation theory assumes we also have '.

We shall also suppose that the problem

We must therefore make trial whether we may not have more success in the tasks of metaphysics, if we suppose that objects must conform to our knowledge " ( Bxvi ).

Moreover, as one British civil servant wrote on August 22, 1938: We have had similar visits from other emissaries of the Reichsheer, such as Dr. Goerdeler, but those for whom these emissaries claim to speak have never given us any reasons to suppose that they would be able or willing to take action such as would lead to the overthrow of the regime.

A strategy-stealing argument for tic-tac-toe goes like this: suppose that the second player has a guaranteed winning strategy, which we will call S. We can convert S into a winning strategy for the first player.

We might suppose from this that Hobbema and Ruisdael, the two great masters of landscape, were united at this time by ties of friendship, and accept the belief that the former was the pupil of the latter.

We argue by contradiction: suppose the new problem is easy to solve.

To obtain a contradiction, suppose R is a decider for E. We will use this to produce a decider S for H ( which we know does not exist ).

We might perhaps suppose the polarisers to be perfect, with output intensity of polariser A proportional to cos < sup > 2 </ sup >( a − λ ), but reject the quantum-mechanical assumption that the function relating this intensity to the probability of detection is a straight line through the origin.

We typically do not know if the asset will have this return ; suppose we assess the risk of the asset, defined as standard deviation of the asset's excess return, as 10 %.

We suppose that high pay, little environmental insult, upward mobility for workers, and stability or growth are among the attributes desired of new activities.

We do not suppose that winter becomes spring, or say that spring becomes summer.

We may suppose that his real motives were a wish to do Justice to the merits of Zi-ruo, and to restore the symmetry of the tablets in the ' Hall of the Great and Complete One ' ( Dacheng-dian ), which had been disturbed by the introduction of the tablet of Zhu Xi in the preceding reign.

We write 1 and 0 for the largest and the smallest element of, respectively.

We define to be the size of the largest collection of disjoint edges in H and to be the size of the smallest edge in.

We can thus compute the smallest index i such that ( x < sub > i </ sub >) ≥ y as follows:

We then have values for the hyperparameters of the approximating distributions of the posterior parameters, which we can use to compute any properties we want of the posterior — e. g. its mean and variance, a 95 % highest-density region ( the smallest interval that includes 95 % of the total probability ), etc.

We are tempted to blame others for our problems rather than look them straight in the face and realize they are of our own making and possible of solution only by ourselves with the help of desperately needed, enlightened, competent leaders.

We can escape from such a difficulty by ruling out the animal as not constituting a trial, but such a solution is not always satisfactory.

We suggest the application of certain data-processing techniques as a solution to the problem.

But now We join Our voice to that of Our predecessor John XXIII of venerable memory, and We make Our own his words: " No statement of the problem and no solution to it is acceptable which does violence to man's essential dignity ; those who propose such solutions base them on an utterly materialistic conception of man himself and his life.

We wish to maximize total value subject to the constraint that total weight is less than or equal to W. Then for each w ≤ W, define m to be the maximum value that can be attained with total weight less than or equal to w. m then is the solution to the problem.

We must disregard the solution.

We feel that this is a satisfactory solution – not only satisfying to the mind, but also, and above all, satisfactory from the humanitarian point of view.

We might therefore expect that the solution of a Toeplitz system would be easier, and indeed that is the case.

We instruct the Council for TRIPS to find an expeditious solution to this problem and to report to the General Council before the end of 2002.

* France-On 20 January 2003, Foreign Minister Dominique de Villepin said, " We think that military intervention would be the worst possible solution ," although France believed that Iraq may have had an ongoing chemical and nuclear weapons program.

We constrain our solution using Lagrange multipliers forming the function:

" We are of those who are convinced that the ultimate solution of this social question is bound to be discovered in the person and life of Christ.

We therefore conclude that the transmitted wave must be a non-vanishing solution to Maxwell's equations that is not a traveling wave, and the only such solutions in a dielectric are those that decay exponentially: evanescent waves.

We want to approximate the solution of the differential equation

We get the solution to the dynamics problem ( up to a factor of ) from the statics problem by Wick rotation, replacing by and the spring constant by the mass of the rock:

" Ultimately, security and material items are cited as the solution to any problem in the country " We want to remind people that there is no problem this country can throw at you that you can ’ t solve with electric fencing and a pedicure.

We may still hope that the ideal-chain, random-coil model will be at least a qualitative indication of the shapes and dimensions of real polymers in solution, and in the amorphous state, as long as there are only weak physicochemical interactions between the monomers.

We will show that: ( i ) there exists a set of linearly independent solutions to the homogeneous system, and ( ii ) that every other solution is a linear combination of these solutions.

We next prove that any solution of must be a linear combination of the columns of.

We take the solution basis found above.

We know what the optimal solution would have been.

We have spoken to the United States about it — it ’ s our understanding that the arrangement was not to be permanent and we ’ re looking to the US State Department to find a permanent solution.

We can construct another solution by setting X ′