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 of the irregularities which have troubled scribes and scholars perhaps merely reflect the everyday usages of the careless and untrained tongues which Plautus heard about him .” Looking at the overall use of archaisms within Plautus, one will notice that they commonly occur in promises, agreements, threats, prologues, or speeches.

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, 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 arise various mistaken beliefs, such as the belief in revelation which he believes not only injures the moral sense, but also " poisons, nay destroys, the divinest feeling in man, the sense of truth ," and the belief in sacraments such as the Lord's Supper, which is to him a piece of religious materialism of which " the necessary consequences are superstition and immorality.

Hence, for eliminativism to be asserted as a thesis, the eliminativist must believe that it is true ; if that is the case, then there are beliefs and the eliminativist claim is false.

Hence, determining a person's system of constructs would go a long way towards understanding him, especially the person's essential constructs that represent very strong and unchangeable beliefs ; and also the constructs a person applies to him / herself.

Hence, popular Islam became an overlay of Quranic ritual and principles upon the vestiges of earlier beliefs — prevalent throughout North Africa — in jinns ( spirits ), the evil eye, rites to ensure good fortune, and cult veneration of local saints.

Hence the Byzantine stories are traditional in their plot structure and setting ( featuring complex turns of events taking place in the ancient Mediterranean, complete with the ancient gods and beliefs ) but are also medieval, clearly belonging to the era of the Crusades as they reflect customs and beliefs of that time.

Hence, those 40 years suggest more strongly than can any set of formulaic tests that few individuals, whatever their system of beliefs, are likely to have understood the monument as amounting, in any significantly detrimental way, to a government effort to favor a particular religious sect, primarily to promote religion over nonreligion, to " engage in " any " religious practic ," to " compel " any " religious practic ," or to " work deterrence " of any " religious belief.

Hence, ideological beliefs created within the culture and other social forces shape the prejudices of the given authoritarian individual.

Hence arise various mistaken beliefs, such as the belief in revelation which he believes not only injures the moral sense, but also " poisons, nay destroys, the divinest feeling in man, the sense of truth ," and the belief in sacraments such as the Lord's Supper, which is to him a piece of religious materialism of which " the necessary consequences are superstition and immorality.

Hence all teachers, good and bad, who have been teaching for a given number of years are paid the same salary.

Hence it follows that the involution within the bundle must be a perspective De Jonquieres involution of order Af and the invariant locus must have a multiple line of multiplicity either Af or Af.

Hence **zg must have either a regulus of Af-fold secants or a regulus of Af-fold secants.

Hence, as some scholars of China suggest, the Xia and the Shang can possibly refer to political entities that existed concurrently, just as the early Zhou is known to have existed at the same time as the Shang.

Hence, cnidarians and ctenophores have traditionally been labelled diploblastic, along with sponges.

Hence, diffraction patterns usually have a series of maxima and minima.

Hence, the wine and the bread are merely symbols ( sometimes referred to as " emblems "), but they have a profound meaning for Jehovah's Witnesses.

" Hence, Anglican jurisdictions have traditionally been conservative in their approach to either innovative doctrinal development or in encompassing actions of the church as doctrinal ( see lex orandi, lex credendi ).

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

Hence the group included supporters of Trotskyism, like Judith Merril and others who would have been deemed far left for the era ( Frederik Pohl became a member of the Communist Party in 1936, but later quit in 1939 ).

Hence GSSPs are usually described in terms of transitions between different faunal stages, though far more faunal stages have been described than GSSPs.

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, Weird Tales may only have owned the rights to at most six of Lovecraft's tales.

Hence, straight hair may have ( initially ) evolved to aid the entry of UV light into the body during the transition from dark, UV-protected skin to pale-white skin.

Hence, Moseley's discovery demonstrated that the atomic numbers of elements are not just rather arbitrary numbers based on chemistry and the intuition of chemists, but rather, they have a firm experimental basis from the physics of their X-ray spectra.

Hence in 1988 it was likely that a solution would have to wait until the war ended.

Hence, Deuterium-free drinking water is considered to have the potential of lowering the risk of cancer caused by extreme radiation exposure of the Martian crew.

" Hence although men had become less forebearing, and although natural pity had already undergone some alteration, this period of the development of human faculties, maintaining a middle position between the indolence of our primitive state and the petulant activity of our egocentrism, must have been the happiest and most durable epoch.

Hence, these fragments are among the oldest objects in the solar system and have preserved information about its early history.

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

Hence, if they have similar masses then their weights will also be similar.

Hence call to mind, come to mind, keep in mind, to have mind of, etc.

Hence, sometimes two syllables have been underlined, as in hige and mægen.

Hence to express the remainder we would have to write, rather than, since equivalence can only be said of common residues with the same sign.

Hence, high input dimensionality typically requires tuning the classifier to have low variance and high bias.