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

Thus, they are the basis of many software vulnerabilities and can be maliciously exploited.

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, there is a good basis for affirming the straightforward and traditional claim that the Epistle to Titus was authentically written by Paul.

Thus a conventionally corrected form of Newcomb's formula, to incorporate the corrections on the basis of mean solar time, would be the sum of the two preceding expressions:

Thus, freethinkers strive to build their opinions on the basis of facts, scientific inquiry, and logical principles, independent of any logical fallacies or intellectually limiting effects of authority, confirmation bias, cognitive bias, conventional wisdom, popular culture, prejudice, sectarianism, tradition, urban legend, and all other dogmas.

Thus, a simple way to change gauge is to use different needles, which is the basis of uneven knitting.

Thus far, no system design has been shown to meet this requirement fully on a technical basis alone.

Thus, solid-state physics forms the theoretical basis of materials science.

Thus, on the basis of remarks made by President Kim Il Sung in 1977 concerning school attendance, the population that year was calculated at 17. 2 million persons.

Thus, on the basis of the budget of 1861, tax collection continued for four years.

Thus, while the outcome of any particular hand significantly involves chance, the long-run expectations of the players are determined by their actions chosen on the basis of probability, psychology and game theory.

Thus, one would expect to find a factor that roughly corresponds to " left " and " right ", as this is the dominant framing for politics in our society, but the basis of Eysenck's " tough / tender-minded " thesis ( the second, " T "- factor ) may well represent nothing beyond an abstract mathematical construct.

Thus, in the predominantly agrarian Qing Dynasty, the " household " was the basis of imperial finance.

Thus, on a weight-for-weight basis they are significantly more energetic than normal condensed explosives.

Jeff Snyder is a spokesman for the view that gun possession is a civil right, and that therefore arguments about whether gun restrictions reduce or increase violent crime are beside the point: " I am not here engaged in ... recommending ... policy prescriptions on the basis of the promised or probable results crime ... Thus these essays are not fundamentally about guns at all.

Thus, many believed that tribes organize links between families ( including clans and lineages ), and provide them with a social and ideological basis for solidarity that is in some way more limited than that of an " ethnic group " or of a " nation ".

Thus, knowledge of paleoecology, palaeogeography, glacial geology and paleoclimatology is important for the recognition and understanding of soil genesis and constitute a basis for predicting the future soil changes.

Thus Tychonoff's theorem joins several other basic theorems ( e. g. that every nonzero vector space has a basis ) in being equivalent to AC.

: Thus, in Bergsland & Vogt ( 1962 ), the authors make an impressive demonstration, on the basis of actual language data verifiable by extra-linguistic sources, that the " rate of change " for Icelandic constituted around 4 % per millennium, whereas for closely connected Riksmal ( Literary Norwegian ) it would amount to as much as 20 %.

Thus in a short time Charles's own cabinet, the Cabal Ministry, went over to the " Dutch " peace party ; Lord Shaftesbury, much shocked by the revelation, even beginning to consider driving out the troublesome House of Stuart entirely and inducing his secretary, John Locke, to further develop the legal concepts which would later be the basis of the Two Treatises of Government, which justified the Glorious Revolution of 1688.

Thus Grosseteste concluded, following very much in what Boethius had argued, that mathematics was the highest of all sciences, and the basis for all others, since every natural science ultimately depended on mathematics.

Thus, solid-state physics forms the theoretical basis of materials science.

Thus, it remains doubtful whether there is any historical basis for the famous ride.

Thus, law has an internal morality that goes beyond the social rules by which valid laws are made.

Thus, this work of Vyasa, called Jaya deals with diverse subjects like geography, history, warfare, religion and morality.

Thus, a major shift in focus, from concern for the individual ’ s moral behavior to concern for the individuals theological practices, occurred with the post-Reformation morality plays.

Thus, there could be a synergy: compounding the inherent fallible nature of the process with the malleability of memory, the potential mendacity of witnesses, the showmanship and ' magic tricks ' involved in trials and advocacy, and the self interest, venality, morality, poor perception and recollection, and ethical standards of the participants.

Thus, this work of Vyasa, called Jaya deals with diverse subjects like geography, history, warfare, religion and morality.

Thus, it was concluded, the temporal authorities must submit to the spiritual authorities, not merely on matters concerning doctrine and morality: " For with truth as our witness, it belongs to spiritual power to establish the terrestrial power and to pass judgment if it has not been good.

Thus, by the criterion of harmony, Shaftesbury refutes Hobbes, and deduces the virtue of benevolence as indispensable to morality.

Thus, while the majority of those who support the current regime may consider criminalisation of politically motivated behaviour an acceptable response when the offender is driven by more extreme political, ideological, religious or other beliefs, there may be a question of the morality of a law which simply criminalises ordinary political dissent.

Thus, not only did they dictate morality, but they also guided readers ' choice of dress and outlined " proper " etiquette.

Thus, this work of Vyasa, called Jaya, deals with diverse subjects like geography, history, warfare, religion and morality.

We can design our life any way we want, but whether we will thrive depends on how well the life fits human predispositions " Thus, the goals of evolutionary psychology overlap with the science of morality.

Thus Spinozism teaches a form of determinism and ecology and supports this as a basis for morality.

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the fictional detective is much more than a simple businessman.

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

Thus in both types attention is focused on the community itself, and its phenomenological life.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

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

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus there is a clearer division of authority, administrative and legislative.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus technical efficiency is achieved at the expense of actual experience.

Thus, there is an added incentive to stay on the job.

Thus, the Span of its ossification was shortened and the center's ability to `` catch up '' in ossification is demonstrated.

Thus T is not diagonalizable.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

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 we do not score the number of bull's-eyes, and the random variable is not the number of successes.

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 Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.