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, any geometric primitives that are provided by the editor are immediately converted to pixels and painted onto the canvas.

Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid's geometric art, I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters.

Therefore, many books and papers on relativistic physics use geometric units exclusively.

Therefore, rather than using elements of a geometric series, a different system of preferred dimensions has evolved in this area, known as " modular coordination ".

Therefore to Helva, the problem that she couldn't open her mouth to sing, among other restrictions, did not bother her.

Therefore, vapor lock is almost never a problem in a vehicle with fuel injection.

Therefore God's present desire is that the problem of sin be solved and that all these things be restored, thus bringing about the earthly and heavenly kingdom of God.

Therefore, designing a smooth V6 engine is a much more complicated problem than the straight-6, flat-6, and V8 layouts.

Therefore functional analysis of the mind alone will always leave us with the mind-body problem which cannot be solved.

Therefore Molniya orbit satellite have been launched, mainly in Russia, to alleviate this problem.

Therefore, its use in the production should not be a problem for vegans.

Therefore, the assertion that an object R → R * is initial in E, that is, that there is a morphism from it to any other element of E, means that the ring R * is a most efficient solution to our problem.

Therefore, preventing hydrate formation appears to be the key to the problem.

Therefore, we have to reword the problem so that the sequential version is in P. That is why this problem required T to be written in unary.

Therefore, for the purposes of locating and fixing bugs, it is vitally important to be able to retrieve and run different versions of the software to determine in which version ( s ) the problem occurs.

Therefore, wear is a major problem in that area.

Therefore, there is an important overflying problem.

Therefore, brute-force search is typically used when the problem size is limited, or when there are problem-specific heuristics that can be used to reduce the set of candidate solutions to a manageable size.

Therefore, by trying this replacement for all edges incident to some chosen vertex of G, the Hamiltonian cycle problem can be solved by at most n Hamiltonian path computations, where n is the number of vertices in the graph.

Therefore, a fundamental problem in knot theory is determining when two descriptions represent the same knot.

Therefore, if King Juan Carlos had decided to follow the Belgian example in 2005 or 2010, a declaration of incapacity would only transfer the problem to Prince Felipe, his heir apparent.

Therefore, most fictional and non-fictional media productions about crime begin by briefly ' sensationalizing ' a concerning event before presenting a non-political resolution, provided by agents of the criminal justice system, to the event and the isolated moral problem it represents.

Therefore ( besides temporary strong discomfort to the animals ) any outbreak in the rich world should not be much more as a localized, cyclical economic problem.

For instance, the problem statement and the solution statement are printed in bold font, the latter is always preceded by the " Therefore :" keyword.

Therefore God's present desire is that the problem of sin be solved and that all these things be restored, thus bringing about the earthly and heavenly kingdom of God.

Therefore, the missing mass problem is not solved by MACHOs.

Therefore, some authors consider that the name " divide and conquer " should be used only when each problem may generate two or more subproblems.