Thus, it was not until two centuries had passed that in 1872 Karl Weierstrass presented the first definition of a function with a graph that would today be considered fractal, having the non-intuitive property of being everywhere continuous but nowhere differentiable.

Thus, intellectual property ensures this right when it comes to production.

Thus, while people have the right to private property, they should give it away as enlightened altruists.

Thus, he saw private property as both essential to liberty and a road to tyranny, the former when it resulted from labour and was required for labour and the latter when it resulted in exploitation ( profit, interest, rent, tax ).

Thus, your watch is your own, but the watch factory belongs to the people. Land, machinery, and all other public utilities will be collective property, neither to be bought nor sold.

Thus again the Paradox shows omniscience to be a self-refuting argument as an attribute or property of such a proposed omniscient entity.

Thus it is assumed that the property is a universal which is distinct from the particular individual who has the property ( MacLeod & Rubenstein, 2006, § 1b ).

Thus, private property continually destroys itself, becoming transformed into communal wealth.

Thus, if rights vested in a property when and where it was purchased, it would not be adversely affected by a later change of domicile.

Thus rationality is seen as a property of patterns of choices, rather than of individual choices: there is nothing irrational in preferring fish to meat only first time, but there is something irrational in preferring fish to meat and preferring meat to fish, regularly.

Thus given a set, a computable function has property F if and only if.

Thus, if a burglar is verbally challenged by the property owner and sustains injury when jumping from a second story window to escape apprehension, there is no cause of action against the property owner even though that injury would not have been sustained but for the property owner's intervention.

Thus, a tax on the sale of property would be considered an indirect tax, whereas the tax on simply owning the property itself would be a direct tax.

Thus, tax collectors often monitor newspaper articles for stories about wealthy people who have lent art to museums for public display, because the artworks have then become subject to personal property tax.

Thus, property taxes tend to be imposed on property owners.

Thus, the coordinates differences ( Δx, Δy, Δz ) and ( Δξ, Δη, Δζ ) are not intrinsic to the rod, but merely reflect the reference frame used to describe it ; by contrast, the length L is an intrinsic property of the rod.

Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.

Thus despite the fact no cigars have been brought into the hotel, each guest can smoke a cigar inside the property.

Thus phones were property of the Bell System, located on customers ' premises – hence, customer-premises equipment.

Thus, to cite but one example, the Pax Britannica of the nineteenth century, whether with the British navy ruling the seas or with the City of London ruling world finance, was strictly national in motivation, however much other nations ( e.g., the United States ) may have incidentally benefited.

Thus, Margenau remarks: `` A large number of unrelated epicycles was needed to explain the observations, but otherwise the ( Ptolemaic ) system served well and with quantitative precision.

Thus, the Church was born and because of its intrinsic character was soon identified as a conservative institution, determined to resist the forces of change, to identify itself with the political rulers, and to maintain a kind of splendid isolation from the masses.

Thus, when the Russians sent up their first sputnik, American chagrin was human enough, and American determination to put American satellites into orbit was perfectly understandable.

Thus, a finding of conspiracy to restrain trade or attempt to monopolize was excluded from the Court's decision.

Thus, in the last few years, a number of programs which looked very promising at the time their development was commenced have since been completely eliminated.

Thus was invented the single thread sewing machine, which Mr. Gibbs in partnership with Mr. Willcox decided to bring to Brown & Sharpe with the proposal that the small company undertake its manufacture.

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

Thus, the energy transferred from the arc to the anode was partly fed back into the arc.

Thus, the dotted line shown in figure 4 was taken as typical for the temperature distribution for all blowing rates.

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

Thus to has light stress both in that was the conclusion that I came to and in that was the conclusion I came to.

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

Thus, in the immemorial way -- in the way of the right hand that knows and the left that does not -- was the stage set for tragedy at Bari.

Thus at the same time that William Henry Harrison was preparing to pacify the aborigines of Indiana Territory and winning fame at the battle of Tippecanoe, Anglo-Saxon settlement made a great leap into the center of the North American continent to the west of the American agricultural frontier.

Thus, when Dartmouth's Winter Carnival -- widely recognized as the greatest, wildest, roaringest college weekend anywhere, any time -- was broadcast over a national television hookup, Prexy John Sloan Dickey appeared on the screen in rugged winter garb, topped off by a tam-o'-shanter which he confessed had been acquired from a Smith girl.

Thus when Premier Khrushchev intimated even before inauguration that he hoped for an early meeting with the new President, Mr. Kennedy was confronted with a delicate problem.

Thus `` America '', the most widely sung of the patriotic songs, was written by a New England Baptist clergyman, Samuel Francis Smith ( 1808-1895 ), while a student in Andover Theological Seminary.

Thus, the Mahayana metaphysic of mystical union for salvation was distilled down to a bare self-seeking, and for this reason, the mystic in Asia did not long remain in isolated contemplation.

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

Thus, the masculine animate infinitive dabhumaksanigalu'ahai, meaning to live, was, in the perfect tense, ksu'u'peli'afo, and, in the future, mai'teipa.

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.