( Pp. 228-229 ) in any event, it is obvious that the anti-trust laws did not prevent the formation of some of the greatest financial empires the world has ever known, held together by some of the most fantastic ideas, all based on the fundamental notion that a corporation is an individual who can trade and exchange goods without control by the government ''.

However, a different notion of compactness altogether had also slowly emerged at the end of the 19th century from the study of the continuum, which was seen as fundamental for the rigorous formulation of analysis.

Even though the three processes mentioned above proved to be equivalent, the fundamental premise behind the thesis — the notion of what it means for a function to be effectively calculable — is " a somewhat vague intuitive one ".

The Albigensians, more commonly known as the Cathars, were a heretical gnostic sect, holding that matter was evil and only spirit was good ; this was a fundamental challenge to the notion of incarnation, central to Roman Catholic theology.

A computer-aided proof produced in 1976 by Kenneth Appel and Wolfgang Haken makes fundamental use of the notion of " discharging " developed by Heesch.

Groups share a fundamental kinship with the notion of symmetry.

The debate about this notion as regards physicalism is to what extent mental phenomena exist independently of their ( supposed ) fundamental lowest level-the physical.

Influential to thinkers associated with Postmodernism are Heidegger's critique of the subject-object or sense-knowledge division implicit in Rationalism, Empiricism and Methodological Naturalism, his repudiation of the idea that facts exist outside or separately from the process of thinking and speaking them ( however, Heidegger is not specifically a Nominalist ), his related admission that the possibilities of philosophical and scientific discourse are wrapped up in the practices and expectations of a society and that concepts and fundamental constructs are the expression of a lived, historical exercise rather than simple derivations of external, apriori conditions independent from historical mind and changing experience ( see Johann Gottlieb Fichte, Heinrich von Kleist, Weltanschauung and Social Constructionism ), and his Instrumentalist and Negativist notion that Being ( and, by extension, reality ) is an action, method, tendency, possibility and question rather than a discreet, positive, identifiable state, answer or entity ( see also Process Philosophy, Dynamism, Instrumentalism, Pragmatism and Vitalism ).

In axiomatic set theory the fundamental concept of set is an example of a primitive notion.

IV, p. 164 ): " The fundamental tenet of the Vedânta school consisted not in denying the existence of matter, that is solidity, impenetrability, and extended figure ( to deny which would be lunacy ), but in correcting the popular notion of it, and in contending that it has no essence independent of mental perception ; that existence and perceptibility are convertible terms.

In either approach, the fundamental notion is that of an isotropic subspace W. Each construction depends on an initial freedom in choosing this subspace.

John Locke's conception of the social contract differed from Hobbes ' in several fundamental ways, retaining only the central notion that persons in a state of nature would willingly come together to form a state.

It also discusses what it means to communicate, how knowledge can be represented and stored, the methods and limitations of symbolic representation, and even the fundamental notion of " meaning " itself.

The notion of an " incorporeal potency " is similar to that of " action at a distance " except the former notion remained purely qualitative and there is no inkling of the fundamental " action and reaction " principle.

More profoundly, Shakespeare became a source, by way of its dramatic truth, for Berlioz ' fundamental notion of expressive truth ; this was how he could call Romeo and Juliet " the supreme drama of my life.

In general, the objects and arrows may be abstract entities of any kind, and the notion of category provides a fundamental and abstract way to describe mathematical entities and their relationships.

The notion of a Noetherian ring is of fundamental importance in both commutative and noncommutative ring theory, due to the role it plays in simplifying the ideal structure of a ring.

Structure is a fundamental, tangible or intangible notion referring to the recognition, observation, nature, and permanence of patterns and relationships of entities.

Those who argue classism is especially pervasive or fundamental to the society that they live in often identify classism as the expression of systematic economic exploitation by the ' higher ' classes, and may connect it with an explicit notion of class warfare.

All proofs below use the notion of the adjugate matrix of an n × n matrix M. This is a matrix whose coefficients are given by polynomial expressions in the coefficients of M ( in fact by certain ( n − 1 )×( n − 1 ) determinants ), in such a way that one has the following fundamental relations

In response, it has been argued that the notion of the Duplessis " black years " is a myth propagated by all subsequent major political actors in Quebec due to a fundamental aversion to Catholic church-oriented traditionalist patterns of development, with dominant intellectual movements combining various elements of this dislike.

However, they display certain features that make them fundamental in exploring the notion of diagonalizability of certain operators on vector spaces.

The code that performs hash, compare, or extend operations must also be protected — in this context, the notion of an immutable root-of-trust holds that the very first code to measure security properties of a system must itself be trusted to ensure that a rootkit or bootkit does not compromise the system at its most fundamental level.

Children, conditioned by this mistaken notion, have feared stepmothers, while adults, by their antagonistic attitudes, have made the role of the substitute parents a difficult one.

" Perhaps some notion like " expression " ( in Croce ’ s theories ) or " counter-environment " ( in McLuhan ’ s theory ) can replace the previous role of beauty.

The 15th century exploration of America by European explorers had an important role in formulating new notions of the Occidental, such as, the notion of the " Other ".

One of several views of epistemology, the study of human knowledge, along with rationalism, idealism, and historicism, empiricism emphasizes the role of experience and evidence, especially sensory perception, in the formation of ideas, over the notion of innate ideas or traditions ; empiricists may argue however that traditions ( or customs ) arise due to relations of previous sense experiences.

Andrey Markov introduced the notion of Markov chains ( 1906 ), which played an important role in stochastic processes theory and its applications.

Thus, in place of God's role as guarantor of the coherence of the world, Kant posits a faculty of reason structured by the forms of our intuition ( our sense of time and space ) and the categories of our understanding ( like the notion of cause and effect ).

In an axiomatic theory or other formal system, the role of a primitive notion is analogous to that of axiom.

Other historians note debate about Shaka's role as a uniter versus a usurper of traditional Zulu ruling prerogatives, and the notion of the Zulu state as a unique construction, divorced from the localised culture and the previous systems built by his predecessor Dingiswayo.

In some discourses, Wright argued, the role of the truth predicate might be played by the notion of superassertibility.

Combinatory logic was developed with great ambitions: understanding the nature of paradoxes, making foundations of mathematics more economic ( conceptually ), eliminating the notion of variables ( thus clarifying their role in mathematics ).

The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.

Thematic role is a linguistic notion, which may refer to:

The notion of purification ( cleaning one's soul from all evil things and trying to reach Nirvana and to become immortal in Nirvana ) plays an important role in Buddhism.

Quinto expressed interest in the role because of the duality of Spock's half-human, half-Vulcan heritage, and how the character " is constantly exploring that notion of how to evolve in a responsible way and how to evolve in a respectful way.

Elliott argues that this mistaken notion of his role as king ultimately leads to Richard's failure.

A neurocognitive model — the notion that the basal ganglia plays a role in habit formation and that the frontal lobes are critical for normally suppressing or inhibiting such habits — sees trichotillomania as a habit disorder.

The notion that an ancient Egyptian priestly elite tracked the precessional cycle over many thousands of years plays a central role in the theories expounded by Robert Bauval and Graham Hancock in their 1996 book Keeper of Genesis.

Vico, in The New Science, posited a view of language as fundamentally figurative, and introduced into Enlightenment discourse the notion of the role of the imagination in creating meaning.

The role of nobles in the Feudal System had yielded to the notion of the Divine Right of Kings during the Middle Ages ( in fact, this consolidation of power from the land-owning nobles to the titular monarchs was one of the most prominent themes of the Middle Ages ).

Parnell Bradbury, writing in The Times thought Le Mesurier had played the role " extraordinarily well ", although Harold Hobson, writing in The Sunday Times thought that " the trouble with Mr. John Le Mesurier's Dr. Weston is that he approaches the man too snarlingly ... is a notion of genius that would be unacceptable anywhere outside Victorian melodrama ".

This peace didn't last very long and it soon became apparent that the bà role had become outdated ; the four major states had each acquired their own spheres of control and the notion of protecting Zhou territory had become less cogent as the control over ( and the resulting cultural assimilation of ) non-Zhou peoples, as well as Chu's control of some Zhou areas, further blurred an already vague distinction between Zhou and non-Zhou.

This notion has a strong connection with Lyapunov stability, where the storage functions may play, under certain conditions of controllability and observability of the dynamical system, the role of Lyapunov functions.

Chen's notion of the CCP as a " ruling party " is central to the redefinition of the role of the Party in Jiang Zemin's Three Represents.