Therefore, p belongs to both convex hulls, completing the proof.

Therefore, due to their much larger, longer waterline length, ships had much faster hull speeds, and could run down or away from any contemporary sloop or other marconi rig, even if it pointed more upwind.

Therefore many competitive boats have carbon blocks put in between the hull and 2 securing nuts thus spreading the forces over a larger area.

Therefore, counting the turns of the cups over a set time period produced the average wind speed for a wide range of speeds.

Therefore, after combining like terms, the coefficient of x < sup > n − 2 </ sup > y < sup > 2 </ sup > will be equal to the number of ways to choose exactly 2 elements from an n-element set.

Therefore, communication is social interaction where at least two interacting agents share a common set of signs and a common set of semiotic rules.

Therefore, it is reasonable to believe that if we set out to be ' our brother's keeper ,' we would often bungle the job and end up doing more mischief than good.

Therefore, the set of all equivalence classes of forms a partition of: every element of belongs to one and only one equivalence class.

Therefore, every educational program that desires to improve students ' outcomes in political, health and economic behavior should include a Socratically taught set of classes to teach logic and critical thinking.

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, each slot of a hash table is associated with ( implicitly or explicitly ) a set of records, rather than a single record.

Therefore, the whole set is actually simpler.

Therefore every function on such a set is a net.

Therefore, after integration, extensions can be seen as part of the browser itself, tailored from a set of optional modules.

Therefore, to obtain a full set of Fourier transform data, it is necessary to rotate the crystal through slightly more than 180 °, or sometimes less if sufficient symmetry is present.

Therefore, a set of real numbers is bounded if it is contained in a finite interval.

Therefore, depending on how we modify the axiom scheme of comprehension in order to avoid Russell's paradox, arguments such as the non-existence of a set of all sets may or may not remain valid.

Therefore, we can ask if there is a set whose cardinality is " between " that of the integers and that of the reals.

Therefore some explained that miracles were in fact natural events that had been set up by God at the beginning of time.

Therefore, if there are more than two Fatou domains, each point of the Julia set must have points of more than two different open sets infinitely close, and this means that the Julia set cannot be a simple curve.

Therefore, any set covered by this subcover must also be bounded.

Therefore, in any geometric problem we have an initial set of symbols ( points and lines ), an algorithm, and some results.

Therefore the distinction between aneuploidy and polyploidy is that aneuploidy refers to a numerical change in part of the chromosome set, whereas polyploidy refers to a numerical change in the whole set of chromosomes.

Therefore, New Keynesian models assume instead that firms use their market power to maintain their prices above marginal cost, so that even if they fail to set prices optimally they will remain profitable.

Therefore, one may alternatively define a group action of G on X as a group homomorphism from G into the symmetric group Sym ( X ) of all bijections from X to X.

Therefore SgOX < sub > 4 </ sub > ( X = F, Cl ) and SgO < sub > 2 </ sub > X < sub > 2 </ sub > ( X = F, Cl ) should be possible.

Therefore, the router has to transition to Active state and ask its neighbors for a new route to the destination X.

Therefore, there is no general way to translate an instance of X to an instance of Y with the same answer.

Therefore, if one would give the product topology of R < sup > N </ sup > where the topology of R is the usual topology rather than the discrete one, then the above limit would converge to exp ( X ).

Therefore, if running Mac OS X 10. 5. x, it is now impossible to run any Mac version of FrameMaker using Apple-supplied software.

* Therefore, every X is a Z.

Therefore, if Y is an unprovable statement in a formal system, there is no statement X in that system such that X is equivalent to the implication ( X → Y ).

Therefore, as n approaches infinity, goes to zero and < math > R < I ( X ; Y )-3

Therefore, X is reflexive as topological vector space if and only if it is reflexive as normed space, namely, when the injection J is bijective.

Therefore, X is true for E, F, G, etc.

Therefore, a citizen of Country X is superior to a citizen of Country Y.

Therefore, the major product of the addition of HX ( where X is some atom more electronegative than H ) to an alkene has the hydrogen atom in the less substituted position and X in the more substituted position.

Therefore γ is null-homotopic in C, so that the kernel of p < sub >#</ sub >: π < sub > 1 </ sub >( C, c ) → π < sub > 1 </ sub >( X, x ) is trivial and thus p < sub >#</ sub >: π < sub > 1 </ sub >( C, c ) → π < sub > 1 </ sub >( X, x ) is an injective homomorphism.

Therefore, one argues that the most likely number of non-compact ( large ) spatial dimensions is three.

Therefore many breaks stop voluntarily with three hoops and the peg still to run.

Therefore, The Indian Army, from all three directions of the province, entered in the East Pakistan.

Therefore, during the first three months of 1688, hundreds of those asked the three questions who gave hostile replies were dismissed.

Therefore, three wealthy business men Ibrahim Al-Mudhaf, Helal Al-Mutairi, and Shamlan Ali bin Saif Al-Roumi ( brother of Hussain Ali bin Saif Al-Roumi ), led a protest against Mubarak by making Bahrain their main trade point, which negatively affected the Kuwaiti economy.

Therefore, the first three give an idea of the seasons whereas the last two give an idea of the position among the constellations of the full moon.

It is the business of the pope to look after the interests of the Roman empire, since the empire derives its origin and its final authority from the papacy ; its origin, because it was originally transferred from Greece by and for the sake of the papacy ... its final authority, because the emperor is raised to his position by the pope who blesses him, crowns him and invests him with the empire .... Therefore, since three persons have lately been elected king by different parties, namely the youth son of Henry VI, Philip Hohenstaufen, brother of Henry VI, and Otto Brunswick, of the Welf family, so also three things must be taken into account in regard to each one, namely: the legality, the suitability and the expediency of his election ...... Far be it from us that we should defer to man rather than to God, or that we should fear the countenance of the powerful .... On the foregoing grounds, then, we decide that the youth should not at present be given the empire ; we utterly reject Philip for his manifest unfitness and we order his usurpation to be resisted by all .... since Otto is not only himself devoted to the church, but comes from devout ancestors on both sides ..... therefore we decree that he ought to be accepted and supported as king, and ought to be given the crown of empire, after the rights of the Roman church have been secured.

Therefore, it is necessary to either stack polyester protected photographs horizontally within a box, or bind them in a three ring binder.

Therefore, if each of the three fences in a triple combination were knocked down, the rider would receive 12 faults ( 4 per fence, instead of 4 faults for the entire obstacle.

Therefore, three eclipse records indicate that Romulus reigned from 746 BC to 709 BC.

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, any surface that is not in line with the three major axis needs its own projection plane to show the features correctly.

Therefore, the three vectors

Therefore those of the first creation, in return for the honour, were each required to pay for the upkeep of thirty soldiers for three years amounting to £ 1095, in those days a very large sum.

Therefore the space is recommended in the SI / ISO 31-0 standard, and the International Bureau of Weights and Measures states that " for numbers with many digits the digits may be divided into groups of three by a thin space, in order to facilitate reading.

Therefore, the left-handed Taylor partnered the right-handed Marsh, while Boon batted at number three.

Therefore some method of isotope separation based on the weight of three neutrons must be performed to enrich ( isolate ) uranium-235.

Therefore, halakha allowed for the absolution from a vow (' hattarat nedarim ') which might be performed only by a scholar, or an expert on the one hand, or by a board of three Jewish laymen on the other.

All known elementary particles, including quarks, have charges that are integer multiples of e. Therefore, one can say that the " quantum of charge " is e. In this case, one says that the " elementary charge " is three times as large as the " quantum of charge ".

Therefore, years may have one of three lengths – 354, 355 or 384 days – yet retain a nominal length of twelve months.

: Therefore the plots which had previously been formed separately, often by groups of two or three, were united in a general conspiracy, since even the populace no longer were pleased with present conditions, but both secretly and openly rebelled at his tyranny and cried out for defenders of their liberty.

Therefore, the Separatists commenced three years of difficult negotiations in England to seek permission to settle in the northern parts of the Colony of Virginia ( which then extended north to what would eventually be known as the Hudson River ).