Hence the three defining properties of equivalence relations can be proved mutually independent by the following three examples:

Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and ( following Newton's first law of motion ), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly — that is, in a straight line and at constant speed.

Hence, according to Einstein's field equations, R grew rapidly from an unimaginably hot, dense state that existed immediately following this singularity ( when R had a small, finite value ); this is the essence of the Big Bang model of the universe.

Hence the following system describes PLL

Hence the following figures should be treated with caution, especially those for the Carthaginian side.

Hence, " Freddy " was released as Francis ' first single, which turned out to be a commercial failure, just as her following eight solo singles.

Hence if a player pushed the high score up to say 250, 000 ( needed a really good player ), any novice player following would get thoroughly wiped out for several games due to the increased difficulty level, and would have to play until it dropped back down.

Hence the following dilemma: Either must be held to be an impossible expression in general, or else the meaning of the fundamental symbol of algebra must be extended so as to include rational fractions.

Hence the coin was not minted in the following two reigns.

Hence, following Lanfanc's death in 1090, a number of bishops took advantage of the vacancy to obtain secular constitutions for their cathedrals-Lincoln, Sarum, Chichester, Exeter and Hereford ; while the major urban cathedrals of London and York always remained secular.

Hence, the following term in the denominator of the gain equation:

Hence, the following decomposition

Hence if we now take, the foreign interest rate,, the domestic interest rate, and the rest as above, we get the following results.

Instead, Kripke insists the conclusion is explicitly stated by § 202, which reads “ Hence it is not possible to obey a rule ‘ privately ’: otherwise thinking one was obeying a rule would be the same as obeying it .” Further, Kripke identifies Wittgenstein ’ s interests in the philosophy of mind as being related to his interests in the foundations of mathematics, in that both subjects require considerations concerning rules and rule following.

Hence, the mission following STS-114 is STS-121.

Hence the application of telematics is with any of the following:

This he did as a Police Inspector, following up on the case of Whizzo's Chocolates ( Hence his name, praline being a kind of hazelnut chocolate ), which produced such gems as Cockroach Cluster, Anthrax Ripple, and the titular Crunchy Frog.

Hence they aimed firstly to lay the foundation of administration in a restricted manner with the following basic objectives –

Hence, applicants must provide evidence of their English language proficiency in one of the following ways:

Hence, given the radius, r, center, P < sub > c </ sub >, a point on the circle, P < sub > 0 </ sub > and a unit normal of the plane containing the circle,, one parametric equation of the circle starting from the point P < sub > 0 </ sub > and proceeding in a positively oriented ( i. e., right-handed ) sense about is the following:

Hence, some of the following information may seem a bit contradictory, especially if the assertion that two names are " synonyms " is misconstrued as an assertion that the two names mean exactly the same thing.

Hence, a discourse is composed of semiotic sequences ( relations among signs ) between and among objects, subjects, and statements.

Hence, once signed, all statements of fact ( usually found in the opening recital which sets out the reason ( s ) for making the deed ) are conclusive evidence against the parties who are estopped from asserting otherwise.

Hence many philosophical problems are rejected as pseudo-problems which arise from logical mistakes, while others are re-interpreted as empirical statements and thus become the subject of scientific inquiries.

" Hence, the many statements that Ethiopians engaged in relations ... with their siblings or parents.

Hence the scales measuring individual differences on authoritarianism often include the criteria attitudinal statements of political ideologies.

Hence starburst activity usually lasts for only about ten million years, a relatively brief period in the history of a galaxy.

Hence, scientists and physicians sometimes talk for example about the ( geno ) type of a particular cancer, that is the genotype of the disease as distinct from the diseased.

Hence he began transmitting military intelligence to the USSR, though the historical record is unclear about exactly when he started.

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

Hence, some scholars also speak about " Caithness Norn ", but others avoid this.

Hence it has three main elements: description of the phenomena ; developing a general theory about the causes of various types of change ; and applying those theories to specific facts.

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 the paradox, because typically programmers are “ satisfied with whatever language they happen to use, because it dictates the way they think about programs ”.

Hence, nations can be very careful about terming an agreement to be a treaty.

Hence, from the Bayesian-Carnapian point of view, the observation of a non-raven does not tell us anything about the color of ravens, but it tells us about the prevalence of ravens, and supports " All ravens are black " by reducing our estimate of the number of ravens which might not be black.

Hence, the book's theme of homophobia was changed to one about racism and antisemitism.

Hence, the formation of helium-4 is delayed until the universe becomes cool enough to form deuterium ( at about T = 0. 1 MeV ), when there is a sudden burst of element formation.

Hence observations about deuterium abundance suggest that the universe is not infinitely old, which is in accordance with the Big Bang theory.

Hence is language essential to the imposition, establishment, and functioning of the cultural hegemony that influences what and how people think about the status quo of their society.

Hence the bare instrumentalist view of quantum mechanics outlined in the previous section is not an interpretation at all, for it makes no claims about elements of physical reality.

Hence, baptism is not performed until one is able to understand and accept the message of the gospel, typically at about age thirteen.

Hence the Almagest cannot have been completed before about 150, a quarter century after Ptolemy began observing.

Hence, based on this, the earliest known texts to have spoken about karma, sansara and Moksha or Mukti, are the Vedas and other Dharmic Texts.

Hence, what do you think about the person who himself acts upon it?

Hence the natural inference that the country about these great lakes was the ancient residence of the Aztecs.

Hence it was only in the 1920s that Alma Mahler-Werfel asked the composer Ernst Krenek to make a fair copy of Mahler's orchestral draft for a festival of performances of Mahler works, and at about the same time some of the manuscripts were published by the company of Paul Zsolnay in facsimile ( 1924 ).

Hence the theorem about Poincaré invariant is a generalization of the Liouville's theorem.

Hence Paul could use the term Christos with no confusion about who it referred to, and as in 1 Corinthians 4: 15 and Romans 12: 5 he could use expressions such as " in Christ " to refer to the followers of Jesus.