Thus 4, 000, 000, which has a logarithm ( in base 10 ) of 6. 602, has 7 as its nearest order of magnitude, because " nearest " implies rounding rather than truncation.

Thus a figure of 11 million enslaved people transported to the Americas is the nearest demonstrable figure historians can produce.

Thus, the writer arranged the planet so its northern hemisphere's midsummer occurs when it is nearest its sun.

Thus, the granite batholiths are typically found at the center of local mountain ranges, while the much older metamorphic gneiss is usually found lower in the mountains, and limestone layers are mostly found in the foothills nearest the Jefferson River.

Thus, the HTMLHelp software could immediately seek to the nearest 64 kilobyte interval and start decoding from there, rather than decoding from the beginning of the compressed datastream at all times.

where is the graph distance between vertices w and v. Thus, this sum is over the nearest neighbors of the vertex v. For a graph with a finite number of edges and vertices, this definition is identical to that of the Laplacian matrix.

Thus, the exact ratio of ex to em can also vary by font size within a browser if the determined values are rounded to the nearest whole unit.

Thus, paradoxically, the beat writers resort to `` religious '' metaphors: they are in search of mana, the spiritual, the numinous, but not anything connected with formal religion.

Thus the Congress marks a formal recognition of the political system that was central to world politics for a century.

Thus, an axiom is an elementary basis for a formal logic system that together with the rules of inference define a deductive system.

Thus, by 1939, both Church ( 1934 ) and Turing ( 1939 ), neither having knowledge of the other's efforts, had individually proposed that their " formal systems " should be definitions of " effective calculability "; neither framed their statements as theses.

Thus, the only logical possibilities are to accept non-Euclidean geometry as physically real, or to reject the entire notion of physical tests of the axioms of geometry, which can then be imagined as a formal system without any intrinsic real-world meaning.

Thus each polynomial is actually equal to the sum of the terms used in its formal expression, if such a term a < sub > i </ sub > X < sup > i </ sup > is interpreted as a polynomial that has zero coefficients at all powers of X other than X < sup > i </ sup >.

Thus Britain had both a formal Empire based on British rule and an informal one based on the British pound.

Thus, for example, formal notions of causality do not appear in standard texts in classical mechanics.

Thus it was worn with the standard accompaniments for the evening tailcoat at the time: matching trousers, white or black waistcoat, white bow tie, white detachable wing-collar formal shirt and black formal shoes.

Thus no formal system ( satisfying the hypotheses of the theorem ) that aims to characterize the natural numbers can actually do so, as there will be true number-theoretical statements which that system cannot prove.

Thus, in these respects formal power series behave like Taylor series.

Thus far, they have only achieved the formal classification of the phenomena with an elaborate nomenclature — yet do not understand what such activities really mean in a strictly scientific sense.

Thus, Hemingway uses the archaic " thou " ( particularly in its oblique and possessive form ) to parallel the Spanish pronominal " tú " ( familiar ) and " Usted " ( formal ) forms.

Thus, although the Naskapis had never filed a formal statement of claim or similar document, except for a draft history prepared by the late Dr Alan Cooke, the parties to the JBNQA accepted the legitimacy of their claims, and they entered into an agreement-in-principle with the Naskapis in the Spring of 1977 to negotiate an agreement that would have the same principal features as the JBNQA.

Thus, there is a need for formal control to supplement informal control.

Thus, both pre-20th century disciplines were labelled " classical " and modern movements in art which saw themselves as aligned with light, space, sparseness of texture, and formal coherence.

Thus, the formal organization is expected to behave impersonally in regard to relationships with clients or with its members.

Thus, the provinces and parliament have no formal role in such appointments, sometimes a point of contention.

Thus, the formal organization is expected to behave impersonally in regard to relationships with clients or with its members.

Thus, for example, online help systems can usefully employ chatbot techniques to identify the area of help that users require, potentially providing a " friendlier " interface than a more formal search or menu system.

Thus, by the formal definition, the polyhedron is a face of itself.

Thus, the given name was reserved for oneself and one's elders, while the zì would be used by adults of the same generation to refer to one another on formal occasions or in writing ; hence the term " courtesy name ".

Thus, if the solution is to be said to work, then it is to be said to work solely within the given formal system, and not otherwise.

Thus, if the Cl < sup >–</ sup > ion is favored for reduction, then the water reaction is favored for oxidation producing gaseous oxygen, however experiments show gaseous chlorine is produced and not oxygen.

Thus, in aqueous solution, only the + 3 oxidation state is encountered.

Thus, a MLCT results in oxidation of the metal center, whereas a LMCT results in the reduction of the metal center.

Thus, for example, Dexibuprofen, the (+)-( s )- enantiomer of Ibuprofen, can be produced by enantioselective hydroformylation followed by oxidation.

Thus, serum albumin transports fatty acids to organs such as muscle and liver for oxidation when blood sugar is low.

Thus, metals with a low oxidation state for the later metals and mid-oxidation states for the early metals tend to form stable clusters.

Thus, there has come into being a situation in which the state must raise all of its own revenues and, in addition, must give assistance to its local governments.

Thus Af denotes the state of the feed to the R-stage process, and Af the state of the product from the last stage.

Thus, he supported funding to the state to assist the expansion of the East Tennessee and Virginia Railroad.

Thus the necessary and sufficient conditions for the truth of a proposition of law simply involved internal logic and consistency, and that the state's agents used state power with responsibility.

Thus a description of the cat during the course of the experiment — having been entangled with the state of a subatomic particle — becomes a " blur " of " living and dead cat.

Thus, texts like the Annals will often state whether the calendar they use ( the calendar of Lu ) is in phase with the Royal calendar ( used by the Zhou kings ).

Thus, culture has replaced the state as the locus of war.

Thus dubnium is expected to form a stable + 5 state.

Thus, it is easier to state what God is not, than to state what God is:

Thus, the law of " interpenetrating opposites " records the inextricable interdependence of components: the " transformation of quantity to quality " defends a systems-based view of change that translates incremental inputs into alterations of state ; and the " negation of negation " describes the direction given to history because complex systems cannot revert exactly to previous states.

Thus, while a permit to fill non-federal wetlands might require a permit from a single state agency, larger and more complex endeavors — for example, the construction of a coal-fired power plant — might require approvals from numerous federal and state agencies.

Thus, if the rate of any pathway changes, both the excited state lifetime and the fluorescence quantum yield will be affected.

Thus, a piece of iron in its lowest energy state (" unmagnetized ") generally has little or no net magnetic field.

Thus in diplomatic affairs, heads of state are often the first person to greet an important foreign visitor.

Thus in March 1979 Colonel Muammar Gaddafi, who kept absolute power ( until his overthrow in 2011 referred to as " Guide of the Revolution "), after ten years as combined Head of State and Head of government of the Libyan Jamahiriya (" state of the masses "), styled Chairman of the Revolutionary Command Council, formally transferred both qualities to the General secretaries of the General People's Congress ( comparable to a Speaker ) respectively to a Prime Minister, in political reality both were his creatures.

Thus, even when the Electors of Saxony were Catholics during the eighteenth century, they continued to preside over the corpus evangelicorum, since the state of Saxony was officially Protestant.

Thus, the first East Slavic state, Kievan Rus ', emerged in the 9th century along the Dnieper River valley.

Thus, the state required service from both the old and the new nobility, primarily in the military.

Thus the argument also involved the issue of the proper relationship between church and state.