Thus, Sartre rejects what he calls " deterministic excuses " and claims that people must take responsibility for their behavior.

Thus Jean-Paul Sartre, a " comrade " of the Communist party, actively supported the National Liberation Front ( FLN ) ( the porteurs de valises networks, in which Henri Curiel took part ).

Thus, as Sartre often repeated, " Human reality is what it is not, and it is not what it is.

Thus all the sets comprise a general directed graph ( ownership defines a direction ), or network construct.

Thus Kant defines idealism as " the assertion that we can never be certain whether all of our putative outer experience is not mere imagining ".

However, a second definition and usage has historically been in practice in many fields of computer science and information technology, which defines the prefix kilo when used with byte or bit units of data as 1024 ( 2 < sup > 10 </ sup >); this is due to the mathematical coincidence that Thus, in these fields 1 kilobyte is equal to 1 kibibyte, a new unit standardized as part of the binary prefixes to resolve the ambiguity.

Thus, to define particle trajectories, one needs an additional rule that defines which space-time points should be considered instantaneous.

Thus, acceleration is the second derivative of the position vector that defines the trajectory of a particle.

The preceding two paragraphs are an expression in English which unambiguously defines a real number r. Thus r must be one of the numbers r < sub > n </ sub >.

By Taylor's theorem, this is a locally free sheaf of modules with respect to the sheaf of germs of smooth functions of M. Thus it defines a vector bundle on M: the cotangent bundle.

Thus a covering map p: C → X defines a conjugacy class of subgroups of π < sub > 1 </ sub >( X, x ) and one can show that equivalent covers of X define the same conjugacy class of subgroups of π < sub > 1 </ sub >( X, x ).

Thus, b < sub > q </ sub > is a symmetric bilinear form over K with matrix A. Conversely, any symmetric bilinear form b defines a quadratic form

Thus the connection ∇ defines a way of moving elements of the fibers along a curve, and this provides linear isomorphisms between the fibers at points along the curve:

Thus, if a Gaussian process is assumed to have mean zero, defining the covariance function completely defines the process ' behaviour.

cohomologous to c. Thus L defines a unique class in H < sup > 2 </ sup >( G, F < sup >∗</ sup >), which need not be trivial.

Thus the character of Kalyani gets lifted from that of a woman who is a prisoner of destiny to one who defines her own freedom.

The category Top of topological spaces has as morphisms the continuous functions, where a function f is continuous if the inverse image f < sup > − 1 </ sup >( O ) of any open set in the codomain of f is open in the domain of f. Thus any continuous function f from a space X to a space Y defines an inverse mapping f < sup > − 1 </ sup > from Ω ( Y ) to Ω ( X ).

Thus a virtual instrument can either be run as a program, with the front panel serving as a user interface, or, when dropped as a node onto the block diagram, the front panel defines the inputs and outputs for the given node through the connector panel.

Thus I < sup > α </ sup > defines a linear operator on L < sup > 1 </ sup >( a, b ):

Thus I < sup > α </ sup > defines a bounded linear operator from L < sup > p </ sup >( a, b ) to itself.

Thus, Keisler's Elementary Calculus: An Infinitesimal Approach defines continuity on page 125 in terms of infinitesimals, to the exclusion of epsilon, delta methods ; similarly, the derivative is defined on page 45 using infinitesimals rather than an epsilon-delta approach ; finally, integral is defined on page 183 in terms of infinitesimals, while epsilon, delta definitions are not introduced until page 282.

Thus, the PCB is the data structure that defines a process to the operating systems.

Thus Q defines an inner product on dom T. Let H < sub > 1 </ sub > be the completion of dom T with respect to Q. H < sub > 1 </ sub > is an abstractly defined space ; for instance its elements can be represented as equivalence classes of Cauchy sequences of elements of dom T. It is not obvious that all elements in H < sub > 1 </ sub > can identified with elements of H. However, the following can be proved:

Thus, the term could suggest that a dwarf planet is a type of planet, even though the IAU explicitly defines a dwarf planet as not so being.

Thus, the speed ratio of a gear train also defines its mechanical advantage.

Thus, a spatial displacement defines a transformation for Plücker coordinates of lines given by

Thus, Coase defines the firm as " the system of relationships which comes into existence when the direction of resources is dependent on the entrepreneur.

Thus, within Illinois and adjacent parts of Iowa, the Yarmouth Soil ( paleosol ), which defines the Yarmouthian ( Yarmouth ) Interglacial ( Stage ) in Illinois, spans a period of geologic time equivalent to Marine Isotope stages 7, 8, 9, 10, and 11.

Thus while among his own colleagues he seemed merely a hypocritical and arrogant priest, in his relations with his brother humanists, such as Cosimo de ' Medici, he appeared as the student of classical antiquities and especially of Greek theological authors ".

Thus, different combinations of properties and relations produce different objects.

Thus perceptions must already come parcelled into distinct " bundles " before they can be associated according to the relations of similarity and causality: in other words, the mind must already possess a unity that cannot be generated, or constituted, by these relations alone.

Thus there is a natural bijection from the set of all possible equivalence relations on X and the set of all partitions of X.

Thus, there is the idea that in the capitalist mode of production the behaviour of actors in the market economy ( means of production, distribution and exchange, the relations of production ) plays the major role in configuring society.

Thus it broadens the range of sign systems and sign relations, and extends the definition of language in what amounts to its widest analogical or metaphorical sense.

Thus, what he refers to as the multidimensional architecture of language " reflects the multidimensional nature of human experience and interpersonal relations.

Thus the shield was symbolic of the individual soldier's subordination to his unit, his integral part in its success, and his solemn responsibility to his comrades in arms – messmates and friends, often close blood relations.

Thus, the first modern rounding of the cape in 1488 by Portuguese explorer Bartolomeu Dias was a milestone in the attempts by the Portuguese to establish direct trade relations with the Far East ( although in his histories Herodotus proves, disbelievingly, that some Phoenicians had done so far earlier than this ).

Thus, the early 20th century is a period often referred to as the " nadir of American race relations ".

Thus the physical content of the theory has to do not with objects themselves, but the relations between them.

Thus, sexual relations between a man and his mother's sister ( and mother's sister's daughter ) are also considered incestuous, but relations between a man and his father's sister are not.

Thus, he opined that " the German government declared itself ready for friendly relations with the Soviet Union, whereas the English-French war bloc desires a war against the socialist Soviet Union.

Thus, in today's everyday language, the words " ethnic " and " ethnicity " still have a ring of exotic peoples, minority issues and race relations.

Thus friendly relations were established between Rome and Persia which survived for thirty-six years.

Thus one can solve many recurrence relations by rephrasing them as difference equations, and then solving the difference equation, analogously to how one solves ordinary differential equations.

Thus, soft power is often associated with the rise of globalization and neoliberal international relations theory.

Thus High Commissioners could be charged with managing diplomatic relations with native rulers and their states ( analogous to the Resident Minister ), and might have under them several Resident Commissioners or similar agents attached to each state.

Thus, symmetric relations and undirected graphs are combinatorially equivalent objects.

Thus, the human relations movement supported the primacy of organization to be attributed to natural human groupings, communication and leadership.

Thus, fear seems to be an important factor governing the relations between Spartans and Helots.

Thus was born the " idealism " school of international relations.

Thus, the final phase of decolonisation may in fact concern little more than handing over responsibility for foreign relations and security, and soliciting de jure recognition for the new sovereignty.