We can construct symmetric and antisymmetric multi-particle states out of continuous eigenstates in the same way as before.

We can indeed enumerate algorithms to construct a function T, about which we initially assume that it is a function from the natural numbers onto the reals.

) We can construct field operators by applying the Fourier transform to the creation and annihilation operators for these states.

We now wish to construct some two-dimensional Lebesgue measure λ < sup > 2 </ sup > on the plane R < sup > 2 </ sup > as a product measure.

We can then construct the following RP algorithm:

We simply construct the equaliser of two morphisms f and g as the kernel of their difference g − f ; similarly, their coequaliser is the cokernel of their difference.

We now show that it is impossible to construct a 20 ° angle ; this implies that a 60 ° angle cannot be trisected, and thus that an arbitrary angle cannot be trisected.

We can construct a classical continuous random field that has the same probability density as the quantum vacuum state, so that the principal difference from quantum field theory is the measurement theory ( measurement in quantum theory is different from measurement for a classical continuous random field, in that classical measurements are always mutually compatible — in quantum mechanical terms they always commute ).

We assume a fixed background for conceptual simplicity, construct a large spherical shell of mass, and set it spinning in that background.

We have to solve this system for to construct the interpolant The matrix on the left is commonly referred to as a Vandermonde matrix.

We require that f be locally non-zero, meaning that given any point x in the interval and any natural number m, there exists ( we can construct ) a real number y in the interval such that | y-x | < 1 / m and | f ( y )| > 0.

We can, however, construct a representation of the covering group of the Poincare group, called the inhomogeneous SL ( 2, C ); this has elements ( a, A ) where as before, a is a four-vector, but now A is a complex 2 × 2 matrix with unit determinant.

We then construct T ( V ) as the direct sum of T < sup > k </ sup > V for k = 0, 1, 2 ,…

We can then construct another Turing machine that simulates the operation of this machine, along with simulating directly the execution of the machine given in the input as well, by interleaving the execution of the two programs.

We can then construct a projective cogenerator which leads us via to the ring we need for the category of R-modules.

We can construct another solution by setting X ′

We would like to construct a curve whose shape is described by a sequence of p points, which plays the role of a control polygon.

We can easily construct a network of any size recursively using the principles of insertion and selection.

We still lack a working mathematical construct that proves a link between sliding filament theory and Frank-Starling.

We construct an image of ourselves to claim personal identity, and present ourselves in a manner that is consistent with that image.

We ’ ve tried to construct it with transitions of songs going in and out of each other, and I think it's a little bit more expansive than the last record.

As niche construction advocate Derek Bickerton writes, " We could construct our niches without having to wait on interminable rounds of feedback between genes and behavior.

We can construct a story of backdoor illicit liaisons and front door respectability from these fragments and others — Rydberg would hardly be the first, if it were true — but he never spoke openly about his private life at any time, and our best guess would still be guesswork.

We leap from event to event -- including the formation of the posse -- even though the events, in `` reality '' are taking place not in sequence but simultaneously, and not near each other but at a considerable distance.

For example, if I say “ Star Wars is a shitty movie ,” and my friend says, “ Star Wars is not a shitty movie !” We have no shared reality, for in our language, truth lies in only one of our statements and we can forever argue these truths until one of us writes a book and has more authority than the other.

The EPR paper says: " We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

Here, we are told, ' We need to go beyond the pleasure principle, the reality principle, and repetition compulsion to ... the fantasy principle ' - ' not, as Freud did, reduce fantasies to wishes ... consider all other imaginable emotions '; and thus envisage emotional fantasies as a possible means of moving beyond stereotypes to more nuanced forms of personal and social relating.

We keep imprisoned in this yearning when we don't see reality as it is, namely imperfect and ever-changing ;

We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.

We have now grasped the reality of the situation.

We must wake up to the insane reality of our time .... We are all irresponsible, unless we demand from the responsible decision makers that modern armaments must no longer be made available to people whose former battle axes and swords our ancestors condemned.

Daniel Petrie Jr. stated in 2004, " We look at reality TV, which is billed as unscripted, and we know it is scripted.

We understand that shows don't want to call the writers writers because they want to maintain the illusion that it is reality, that stuff just happens.

We can use this consensus as a pragmatic guide, either on the assumption that it seems to approximate some kind of valid reality, or simply because it is more " practical " than perceived alternatives.

We hypothesize that in everyday life consciousness is in a continual state of flux between the general reality orientation and the momentary microdynamics of trance ...

John R. Searle does not elucidate the terms strong and weak in his book The Construction of Social Reality, but he clearly uses them in his Chinese room argument, where he debates the feasibility of creating a computing machine with a sharable understanding of reality, and he adds " We are precisely such machines.

" We have to remember that behind the various caprices of modern historical theories, and as a more profound and primordial reality, there stands the unity of blood and spirit of the white races who created the greatest civilizations both of the East and West, the Iranian and Hindu as well as the ancient Greek and Roman and the Germanic " ( The Doctrine of Awakening, p. 14 ).

We observe reality through her eyes, feel her emotions, share in her pain.

We should not seek for some entity outside function and name it original reality.

We aim to reflect reality.

* Paul Valéry, French poet ( 20th c .) reminds us of the importance of representations and action: " We have always sought explanations when it was only representations that we could seek to invent ", " My hand feels touched as well as it touches ; reality says this, and nothing more ".

:" We will win our freedom because the sacred heritage of our nation and the eternal will of God are embodied in our echoing demands ... when these disinherited children of God sat down at lunch counters they were in reality standing up for what is best in the American dream and for the most sacred values in our Judeo-Christian heritage, thereby bringing our nation back to those great wells of democracy which were dug deep by the founding fathers in their formulation of the Constitution and the Declaration of Independence.

We don ’ t call it white culture, we call it reality .”

We cannot help supposing that there is some experiencer within whose inner life the Whole exists, but only the inevitability of the assumption and not any experiential content assures us of the reality of such an experiencer.

We construe reality constructing constructs.