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.

Hence, many international travelers visit Helsinki on a stop-over between Asia and Europe.

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 the many predictions involving ancient figures such as Sulla, Gaius Marius, Nero, and others, as well as his descriptions of " battles in the clouds " and " frogs falling from the sky.

Hence, not only the ideas of the Muslim political philosophers but also many other jurists and ulama posed political ideas and theories.

Hence many other Christians saw the Anabaptists as subversive of all order.

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.

Hence, many of these countries expressed their support for the Whites, including the provision of troops and supplies.

Hence, many beliefs have formed around this worship, such as the " missing sun " found in many cultures.

Hence, for many large companies this allows you to understand the WHY behind the visitors ' intents when visiting a website or mobile site.

Hence a particular number of CCS can be carried in infinitely many ways as calls are established and cleared over time.

Hence, the band have been cited as an influence by many other musicians.

Hence the long-standing desire of many colonial administrators to establish a unified structure became feasible.

Hence, even having an algorithm, it remains unknown how many moves an optimal solution requires and how many optimal solutions exist for 1000 disks and 10 pegs.

Hence, government services are not centralized in one location, as they are in many American counties.

Hence many industrial sites appeared there.

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, more mature women can be virgins ( The Virgin Queen ), men can be virgins, and potential initiates into many fields can be colloquially termed virgins ; for example, a skydiving " virgin ".

Hence, many of the commercial establishments in this area are designed for long-distance drivers.

Hence the Earth deviates from a perfect sphere by only a third of a percent, sufficiently close to treat it as a sphere in many contexts and justifying the term " the radius of the Earth ".

Hence, Microsoft's and other variants of BASIC constituted a significant and visible part of the user interface of many home computers ' rudimentary operating systems.

Hence, the book is of great value to the student of the Greek dialects, while in the restoration of the text of the classical authors generally, and particularly of such writers as Aeschylus and Theocritus, who used many unusual words, its value can hardly be exaggerated.

Hence it is difficult to conceive of a packing of the atoms in this material in which the oxygen atoms are far from geometrical equivalence.

Hence the totality of singular lines is the T order complex of lines which meet Aj.

Hence it took a prominent part in the Peloponnesian War until the crushing defeat at Idomene ( 426 ) which crippled its resources.

Hence, by metonymy, it would be employed to denote at times the shield which it supported, and at other times a cuirass, or chlamys, the purpose of which it in part served.

Hence, the only complex Banach algebra which is a division algebra is the complexes.

Hence, readers are recommended to consult instead the alphabetical index or the Propædia, which organises the Britannicas contents by topic.

Hence, much has been preserved, quoted by Eusebius, which otherwise would have been destroyed.

Hence, Mark's explicit claim that the Last Supper was a Passover meal is contraindicated by his statement that Joseph of Arimathea bought a shroud for Jesus on Good Friday ; which would not have been possible if it were a festival day.

Hence, the need for setting up an institution which would impart education along nationalist lines was strongly felt by the luminaries of the period.

Hence, the purpose of the Leninist vanguard party is to establish a democratic dictatorship of the proletariat ; supported by the working class, the vanguard party would lead the revolution to depose the incumbent Tsarist government, and then transfer power of government to the working class, which change of ruling class — from bourgeoisie to proletariat — makes possible the full development of socialism.

Hence, with the addition of more, or the contraction, mor, we have the word MOR-MON ; which means, literally, more good.

Hence, the word " minestrone " originates from the Latin word " minestrare " or literally " that which is served ,".

Hence, according to legend, it is a sacred tree in which the soul of Merlin awaits his return.

" 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, in The Sophist Plato argues that Being is a Form in which all existent things participate and which they have in common ( though it is unclear whether ' Being ' is intended in the sense of existence, copula, or identity ); and argues, against Parmenides, that Forms must exist not only of Being, but also of Negation and of non-Being ( or Difference ).

Hence, the question of which is the largest peninsula in Europe is a debatable one, depending on arbitrary human definitions of where the peninsulas begin — and on which century one chooses to consider: sometimes, Scandinavia as a peninsula has not existed.

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 the SECD machine is often presented in a more detailed form, such as Peter Henderson's Lispkit Lisp compiler, which has been distributed since 1980.

A republican form of government is distinguished from a pure democracy, which the Founding Fathers wanted to avoid ; as James Madison wrote in Federalist No. 10, " Hence it is that such democracies have ever been spectacles of turbulence and contention ; have ever been found incompatible with personal security or the rights of property ; and have in general been as short in their lives as they have been violent in their deaths.

Hence it is more likely to have been produced as the result of a relatively recent breakup of a moderate-sized ( or larger ) comet or asteroid, which then further fragmented as the result of collisions between the smaller components and other bodies.