Hence S breaks up into uncountably many orbits under G. Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset X of S with the property that all of its translates by G are disjoint from X.

Now it is easy to convince oneself that the set X could not possibly be measurable for any rotation-invariant countably additive finite measure on S. Hence one couldn't expect to find an algorithm to find a point in each orbit, without using the axiom of choice.

Hence, violence could theoretically end disputes, but alongside it, life.

( see: labour aristocracy, globalization ) Hence, a proletarian revolution of workers and peasants could not occur in the developed capitalist countries, while the imperialist global-finance system remained intact ; thus an underdeveloped country would feature the first proletarian revolution ; and, in the early 20th century, Imperial Russia was the politically weakest country in the capitalist global-finance system.

Hence, an entire line of program code could express the same idea a small number of characters that other programming languages might easily take 5 to 10 times as many characters to express.

" Hence an argument which claimed that the two parties could be viewed as " equally " culpable in a struggle for supremacy, would be advocating " moral equivalence.

Hence, early studies focused on proteins that could be purified in large quantities, e. g., those of blood, egg white, various toxins, and digestive / metabolic enzymes obtained from slaughterhouses.

Hence, a user believing he is consuming two 120 mg pills of MDMA could actually be consuming a dose of PMA that is potentially lethal, depending on the purity of the pill.

Hence, they participated in many of the major public religious roles that non-levitical men could, albeit less often and on a somewhat smaller and generally more discreet scale.

Through the medium of Scott's novels, the violent religious and political conflicts of the country's recent past could be seen as belonging to history – which Scott defined, as the subtitle of Waverley ("' Tis Sixty Years Hence ") indicates, as something that happened at least 60 years ago.

Hence, video could be sharper vertically than horizontally.

Hence, Mediolanum could signify the central town or sanctuary of a particular Celtic tribe.

Hence, Clarence participated in Warwick's schemes, marrying the earl's daughter Isabella, believing he could gain his brother's throne.

Hence temples were placed on hilltops, their exteriors designed as a visual focus of gatherings and processions, while theatres were often an enhancement of a naturally occurring sloping site where people could sit, rather than a containing structure.

Hence, he concluded that homosexuals suffered a degree of sexual perversion because homosexual practices could not result in procreation.

Hence, such artists could be dubbed " the Fifth Beatle " for a single track or two.

Hence the most important export products, tobacco and hazelnut, could not be sold and living standards degraded.

Hence any assistance provided to the Soviets on the Eastern Front could shorten the war.

Hence he and many of his pupils ( in particular Carl Stumpf and Edmund Husserl ) thought that the natural sciences could only yield hypotheses and never universal, absolute truths as in pure logic or mathematics.

Hence, the star must have a companion that could heat gas to the millions of degrees needed to produce the radiation source for Cygnus X-1.

Hence since light could be reduced to lines and points, and thus fully explained in the realm of mathematics, mathematics was the highest order of the sciences.

Hence no real heat engine could realise the Carnot cycle's reversibility and was condemned to be less efficient.

Hence, to the Donatists, a priest who had been an apostate but who repented could speak the words of consecration forever, but he could no longer confect the Eucharist.

Hence Theodore of Tarsus, who had acquired his learning in Byzantine Asia Minor and bore this tonsure, had to allow his hair to grow for four months before he could be tonsured after the Roman fashion, and then ordained Archbishop of Canterbury by Pope Vitalian in 668.

Hence, in a system isolated from its environment, the entropy of that system will tend not to decrease.

Hence Lübeck has seen a slight decrease in population since 2006.

Hence, Duisburg has seen a slight decrease in its population since 2006.

Hence in liquid helium, its ground state energy can decrease by a naturally-occurring increase in its average interatomic distance.

Hence, demand may expand or contract and increase or decrease.

Hence, the barometric pressure dropped by less than 10 hours after the National Hurricane Center stated that the pressure would not decrease significantly within 24 hours.

Hence, when the baroreceptors are activated ( by an increased blood pressure ), the NTS activates the CVLM, which in turn inhibits the RVLM, thus inhibiting the sympathetic branch of the autonomic nervous system, leading to a decrease in blood pressure.

Hence, informed shoplifters, although they decrease their risk of being caught by the EAS, expose themselves to much greater judicial risks if they get caught with tools, booster bags, or while trying to remove tags, as this characterizes intent to steal.

Hence, trade creation's essence is in elimination of customs tariffs on inner border of unifiying states ( usually already trading with each other ), causing further decrease of price of the goods, while there may be a case of new trade flow creation of the goods between the states decided to economically integrate.

Hence, the number of total base pairs is equal to the number of nucleotides in one of the strands ( with the exception of non-coding single-stranded regions of telomeres ).

* Hence, the book contains over 3. 2 billion letters total ;

Hence, the total length increases by one third and thus the length at step n will be ( 4 / 3 )< sup > n </ sup > of the original triangle perimeter: the fractal dimension is log 4 / log 3 ≈ 1. 26, greater than the dimension of a line ( 1 ) but less than Peano's space-filling curve ( 2 ).

Hence total chances are: 22 + 21 + 20 +....+ 1 = 253, so comparing every person to all of the others allows 253 distinct chances ( combinations ): in a group of 23 people there are pairs.

Hence, by 1889, the Romanian state became the owner of all of the lines in the Kingdom of Romania, the railway system having a total length of 1, 377 km.

Hence, the element dεdK < sub > p </ sub > makes a contribution to the emission current density, and the total contribution made by incident electrons with energies in the elementary range dε is thus

Hence if all states are equally probable ( equal energies ) the partition function is the total number of possible states.

Hence, it is ranked first in Quebec and third in Canada for the total number of engineering diplomas awarded annually.

Hence, the reflections occur through total internal reflection so very little light is lost.

Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy and conservation of momentum are obeyed.

Hence, subset-inclusion is only a partial order, as opposed to the total orders given before.

Hence the total run time is.

Hence, the number of total marbles in the urn grows.

Hence, the number of total marbles in the urn decreases.

Hence, the usual estimator, in terms of sample variance, is not used as this estimates the total squared-error loss from both common-and special-causes of variation.

Hence, a GSV Mind has 200 billion times more storage than the total storage created by humans in 2002.

Hence the fractions of the total power contained within the first, second, and third dark rings ( where ) are 83. 8 %, 91. 0 %, and 93. 8 % respectively.

Hence, in a unified organ, four " ranks " ( really tabs or draw-stops ) can be obtained from a total of 97 pipes.

Hence the Ramsey – Boiteux pricing consists into maximizing the total welfare under the condition of non-negative profit, that is, zero profit.

Hence, through the definition of partial pressure and using p < sub > T </ sub > to represent the total pressure and x to represent the mole fraction ;

Hence, on April 2, after leaving the Ochagavía camp to travel to the lower hills of Maipo, the Patriot army emerged organized in three infantry divisions with a total of 396 chiefs and approximately 5, 000 lower-ranked officers and soldiers.

Hence, the time-adjusted value ( or net present value ) of the Ciresi firm's fees, relative to the total award, was enhanced.

Hence, the total energy deviation is.

Hence at any point in time, only a fraction of the total fuel is burning.