Therefore, for any value of T the number of values of f{t} is equal to the ( finite ) number of tangent points corresponding to the argument T plus an odd number.

Therefore, any measures taken in peacetime which will decrease force requirements in war will contribute greatly to success when hostilities occur.

Therefore, neither merit the beatific vision, nor yet are subjected to any punishment, because they are not guilty of any personal sin although they have not received baptism, so still bear original sin.

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

Therefore, any test of a scientific theory must prohibit certain results which will falsify the theory, and expect other specific results which will be consistent with the theory.

Therefore it soon announced and implemented a hostile doctrine against any political dissent, whether inside or outside the party.

Therefore, it is necessary to have the existence of a conflict in public law without any constitutional aspects and no assignment to another jurisdiction.

Therefore, native Caymanians do not have any Amerindian heritage from their own islands ; however, a significant number of Jamaicans have settled in the Cayman Islands over the years, so they and their descendants may have some Amerindian blood via Jamaica.

Therefore, the diagonal of a 4 x 9 lattice does not intersect any other square lattice | lattice points

Therefore strings beginning with C ( or any other capital letter ) would be sorted before strings with lower-case a, b, etc.

Therefore, just as Christianity does not accept that Mosaic Law has any authority over Christians, Judaism does not accept that the New Testament has any religious authority over Jews.

Therefore an optimizer can replace a string copy with a sequence of word moves without any loops, which will be much faster.

Therefore, as outlined in the example above, neither the EPR experiment nor any quantum experiment demonstrates that faster-than-light signaling is possible.

Therefore, General Niazi and Air Marshal Enamul Haque, Commander of Eastern Air Force Command ( EAFC ), were failed to launch any operation in East Pakistan against Indian or its allies.

More precisely, he showed that a random graph on vertices, formed by choosing independently whether to include each edge with probability has, with probability tending to 1 as goes to infinity, at most cycles of length or less, but has no independent set of size Therefore, removing one vertex from each short cycle leaves a smaller graph with girth greater than in which each color class of a coloring must be small and which therefore requires at least colors in any coloring.

Therefore, the first and second rules (" always treat the gun as if loaded ", " never let the muzzle cover non-targets ") apply to any gun, even one loaded with blanks.

Therefore, all this must be kept secret-which rules out any approach to the police or other outside agency.

Therefore, any eigenstate of the electron in the hydrogen atom is described fully by four quantum numbers.

Therefore any electron can interchange with another one with no observable physical change of the system at all.

Therefore " Liberty will abolish interest ; it will abolish profit ; it will abolish monopolistic rent ; it will abolish taxation ; it will abolish the exploitation of labour ; it will abolish all means whereby any labourer can be deprived of any of his product.

Therefore, language, in the absence of translation, comprises a barrier to a worldwide community of debate and opinion, although it is also true that media within any given society may be split along class, political or regional lines.

Therefore, before any interrogation begins, the police must advise the suspect that:

Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces.

Therefore the quiet Sun always coincides with the equatorial zone and its surface is lower during the maximum of the solar cycle.

Therefore, if an electric field, E < sub > inc </ sub >( x, y ) is incident on the aperture, the field produced by this aperture distribution is given by the surface integral:

Therefore, in a solid wire, most of the cross sectional area of the wire is not used to conduct the current, which is in a narrow annulus on the surface.

Therefore, the photosphere is typically used to describe the Sun's or another star's visual surface.

Therefore, identifying regions of upper air divergence is an important step in forecasting the formation of a surface low pressure area.

Therefore, in 1970, the track was renovated and the surface changed to meet the highest international safety requirements that were needed at large events with many spectators.

Therefore, more generally, a map projection is any method of " flattening " into a plane a continuous surface having curvature in all three spatial dimensions.

Therefore, thermal conductance depends on the external dimensions of the crystal and the quality of the surface.

Therefore, when mechanically stimulated — by boat, swimming or waves, for example — a blue sparkling light can be seen emanating from the sea surface.

Therefore, acoelomate organs are not protected from crushing forces applied to the animal ’ s outer surface.

Therefore the ileum has an extremely large surface area both for the adsorption ( attachment ) of enzyme molecules and for the absorption of products of digestion.

Therefore, data for the purpose of the chemical analysis of lunar surface material were obtained only during the first 30 hours of operation.

Therefore all tangent vectors in a point p span a linear space, called the tangent space at point p. For example, taking a 2-dimensional space, like the ( curved ) surface of the Earth, its tangent space at a specific point would be the flat approximation of the curved space.

Therefore, living cells do not interact directly with the biomaterial surface, but with the adsorbed proteins layer.

Therefore, the most important fluid velocities are those inside this very thin region in which the change in velocity can be considered linear with normal distance from the surface.

Therefore, the shape of the open surface of a fluid equals the equipotential plane of the applied outer conservative force field.

Therefore, the integral of the pressure over the area of the horizontal bottom surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the bottom surface.

Therefore, the integral of the pressure over the area of the horizontal top surface of the cube is the hydrostatic pressure at that depth multiplied by the area of the top surface.

Therefore, the genus is an important topological invariant of a Riemann surface.

Therefore, the details of story structures and contents reveal much about the social, cultural, and historical context in which the story-teller exists., Narrative inquiry is conducted with the understanding that stories that people tell are often at the surface of a more complex underlying story.

Therefore the surface area of the sphere must be, or " four times its largest circle ".