Thus, the definition of T < sub > 3 </ sub > may cite T < sub > 0 </ sub >, T < sub > 1 </ sub >, or T < sub > 2½ </ sub > instead of T < sub > 2 </ sub > ( Hausdorffness ); all are equivalent in the context of regular spaces.

" ( Thus is patriotism rewarded ).</ cite >

Servetus sent Calvin several more letters, to which Calvin took offense .< ref > Will Durant < cite > The Story of Civilization: The Reformation </ cite > Chapter XXI, page 481 </ ref > Thus, Calvin's antagonism against Servetus seems to have been based not simply on his views but also on Servetus's tone, which he considered inappropriate.

Thus, a court might cite " the constitution " in forbidding an exercise of power, even though no document actually exists.

Thus, some sources cite the album's release year as 2003.

Thus, on the highroad, a troop of soldiers `` marched in their own dust and sang '', while on the footpath one man walks alone.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

Thus in Prokofieff the Union of Soviet Socialist Republics produced one of the great composers of the Twentieth Century.

Thus it was that Barco, apprehended for mere larceny, now began to suspect that one or another of his murders had been uncovered.

Thus, a low intensity of hypothalamic-cortical discharges prevails in sleep and a high one during wakefulness, resulting in synchronous EEG potentials in the former and asynchrony in the latter condition.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus, the writer decided to hold one experimental section of the functional preparation for marriage course in the spring semester of 1960 exclusively for persons already married -- that is, prerequisite: `` marriage ''.

Thus, when more than one distinct form leads to a particular cell in the X-region, a chain of information cells must be created to accommodate the forms, one cell in the chain for each form.

Thus, one can think of a dictionary entry as a word rather than a form.

Thus the first lines of one of Charles Wesley's hymns are as follows.

Thus, in the aggregate, the odd-lot trader is one who buys at the tops and sells at the bottoms, notwithstanding occasional individual exceptions.

Thus one line in five from The Iliad and The Odyssey is to be found somewhere else in the two poems.

Thus, when specifically permitted, the operand of a given line on the Autocoder coding sheet may be continued in the operand of from one to four additional lines which immediately follow.

Thus, if one accelerometer is properly aligned, the other is also.

Thus a man who is butting a stone wall at the office may become unusually aggressive in bed -- the one place he can still be champion.

Thus there was really an excess of eighteenth-century charm as one of these light-weight pieces followed another on Saturday night.

Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed.

Thus, according to the character Pausanias in Plato's Symposium, Aphrodite is two goddesses, one older while the other younger.

Thus arose the first monastic community, consisting of anchorites living each in his own little dwelling, united together under one superior.

Thus aesthetic judgments might be seen to be based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behavior, conscious decision, training, instinct, sociological institutions, or some complex combination of these, depending on exactly which theory one employs.

Thus, an analog signal is one represented by a continuous stream of data, in this case along an electrical circuit in the form of voltage, current or charge changes ( compare with digital signals below ).

Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

Thus in Mary wrote an account of the trip first strong stress on Mary marks Mary as the first in a series of people who wrote accounts of the trip, strong stress on wrote marks the writing as the first of a series of actions of Mary's concerned with an account of her trip ( about which she may later have made speeches, for example ), and strong stress on trip makes the trip the first of a series of subjects about which Mary wrote accounts.

Thus, in the example cited above Fromm rests his whole case on the premise that the workers are being deprived unconsciously, unknowingly, of fulfillment, and then supports this with survey data reporting conscious, experienced frustrations.

Thus for example Heraclitus ' The Allegorist ' quoted fr. 326 and part of fr. 6, about ships in a storm, in his study on Homer's use of allegory.

Thus for example two separate quotes by Athenaeus were united by Theodor Bergk to form fr. 362.

Thus, for example, V ← V + 1 is commonly understood to be a shorthand for ( V ,( V ) + 1 ).

Thus, for example, fumaroles from the Laguna Caliente crater of Poás Volcano create extremely high amounts of acid rain and fog, with acidity as high as a pH of 2, clearing an area of any vegetation and frequently causing irritation to the eyes and lungs of inhabitants in nearby settlements.

Thus, for example, the English form is is an apparent cognate of German ist, Latin est and Russian < nowiki > jest '</ nowiki >, even though the Germanic, Italic, and Slavic language groups split at least three thousand years ago.

Thus, for example, there are three main isotopes of carbon.

Thus, for example, on the basis of superficial similarities one might suppose that the Latin verb habere and German haben, both meaning ' to have ', were cognates.

Thus, for example, the same equation can be made to produce both a lyrical and melodic piece of music in the style of the mid-nineteenth century, and a fantastically dissonant cacophony more reminiscent of the avant-garde music of the 1950s and 1960s.

Thus, for example, controversies in physics are limited to subject-areas where experiments cannot be carried out yet, whereas Benford's Law implies that controversy is inherent to politics, where communities must frequently decide on courses of action based on insufficient information.

Thus, no two nuclear powers have yet fought a conventional war directly, with the exception of brief skirmishes between for example, China and Russia in the 1969 Sino-Soviet conflict and between India and Pakistan in the 1999 Kargil War.

Thus, for example, the CGS unit of pressure, barye, is related to the CGS base units of length, mass, and time in the same way as the SI unit of pressure, pascal, is related to the SI base units of length, mass, and time:

Thus a line has a dimension of one because only one coordinate is needed to specify a point on it ( for example, the point at 5 on a number line ).

) Thus, for example, a 2x6 rectangle and a 3x4 rectangle are equal but not congruent, and the letter R is congruent to its mirror image.

Thus, for example, Odysseus is represented in Hecuba ( lines 131-32 ) as " agile-minded, sweet-talking, demos-pleasing " i. e. a type of the war-time demagogues that were active in Athens during the Peloponnesian War.

" Thus in the example above, Hecuba presents herself as a sophisticated intellectual describing a rationalized cosmos yet the speech is ill-matched to her audience, Menelaus ( a type of the unsophisticated listener ), and soon it is found not to suit the cosmos either ( her infant grandson is brutally murdered by the victorious Greeks ).

Thus for example two extant plays, The Phoenicean Women and Iphigenia at Aulis, are significantly corrupted by interpolations ( the latter possibly being completed post mortem by the poet's son ) and the very authorship of Rhesus is a matter of dispute.

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, for example, the funerary god Anubis was portrayed as a jackal, a creature whose scavenging habits threatened the preservation of the body, in an effort to counter this threat and employ it for protection.

Thus, for example, in the ( still used ) local North American subdivision paleontologist finding fragments of the trilobite Olenellus would identify the beds as being from the Waucoban Stage whereas fragments of a later trilobite such as Elrathia would identify the stage as Albertan.

Thus, Hayek put the price mechanism on the same level as, for example, language.

Thus, for example, if we can obtain a decomposition of into a hierarchical composition of functions such that,,, as shown in the figure at right, this would probably be considered a highly valuable decomposition.