We have staved off a war and, since our behavior has involved all these elements, we can only keep adding to our ritual without daring to abandon any part of it, since we have not the slightest notion which parts are effective.

We must avoid the notion, suggested to some people by examples such as those just mentioned, that ideas are `` units '' in some way comparable to coins or counters that can be passed intact from one group of people to another or even, for that matter, from one individual to another.

It is a notion which contains a gratuitous insult, implying, as it does, that Negroes can make no move unless they are manipulated.

( 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 ''.

With this alternate notion of choice function, the axiom of choice can be compactly stated as

The notion of the Kolmogorov complexity can be used to state and prove impossibility results akin to Gödel's incompleteness theorem and Turing's halting problem.

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

The notion of blackness can also be extended to non-black people.

Christopher Hitchens was offended by the notion of Clinton as the first black president noting " we can still define blackness by the following symptoms: alcoholic mothers, under-the-bridge habits ... the tendency to sexual predation and shameless perjury about the same ".

This can be expressed more precisely by the notion of expected value, which is uniformly negative ( from the player's perspective ).

The central concept which is needed for this purpose is called categorical limit, and can be dualized to yield the notion of a colimit.

The dissenters were discontented with the general leftward trend in USCJ policies over the previous decades, such as " prayer book revision, egalitarianism, redefining halakhic boundaries of sexual relationships, and advocacy of Israel accepting conversions that are non-halakhic even by Conservative standards "., and the Union suggests that " The Conservative Movement thus appears to endorse the notion that changing societal norms can supersede the proper application of halakhic sources ".

Cofinality can be similarly defined for a directed set and is used to generalize the notion of a subsequence in a net.

This notion can be extended to any interaction between the impinging particle and the atoms in the target.

Thus, Judaism rejects the notion that anyone can or should die for anyone else's sin.

This notion can also be defined locally, i. e. for small neighborhoods of points.

This divine right is called Daulat, and although presently, the notion of divine right is somewhat obsolete, one can still see banners and posters with pictures of the reigning sultan with words Daulat Tuanku, similar to the European proclamation of " Long live the King ", on streets and buildings.

* Bundles of groups, group actions, sets, and equivalence relations can be regarded as special cases of the notion of groupoid, a point of view that suggests a number of analogies ;

Thus, the only logical possibilities are to accept non-Euclidean geometry as physically real, or to reject the entire notion of physical tests of the axioms of geometry, which can then be imagined as a formal system without any intrinsic real-world meaning.

The boldest, most radical notion in the book is [...] the belief that the individual can and should proceed toward truth by means of his own powers of perception and reasoning ; and that he can in this way discover truths previously unknown.

Economies of scale is related to and can easily be confused with the theoretical economic notion of returns to scale.

In practice, the difference between a mathematical function and the notion of a function used in imperative programming is that imperative functions can have side effects that may change the value of program state.

It does have a notion of " generator ", which amounts to a function accepting a function as an argument, and, since it is an assembly-level language, code can be used as data, so IPL can be regarded as having higher-order functions.

Yet, after Rousseau had given the social contract a new twist with his notion of the General Will, the same philosophy, it may be said, became the idea source of the French Revolution also.

When combined with the metaphysical notion that pure forms of this universe are best appreciated when least embodied in a material substratum, it becomes clear that while earth will be dross on a scale of material-formal ratios, celestial bodies will be of a subtle, quickened, ethereal existence, in whose embodiment pure form will be the dominant component and matter will be absent or remain subsidiary.

In she has it in for George dominant stress will ordinarily be on in, where the notion of stored-up antipathy seems to center.

In such a case, any attitude would be as fitting or unfitting as any other, which means that the notion of fitness has lost all point.

When he heard of his brothers' anger, Palfrey was still hopeful that they could be persuaded to accept his notion of paying wages.

They would like to convey the notion something is being done, even though it is something they know to be ineffectual.

This is the notion that particular cultures should not be judged by one culture's values or viewpoints, but that all cultures should be viewed as relative to each other.

Notably, for skewed distributions, the arithmetic mean may not accord with one's notion of " middle ", and robust statistics such as the median may be a better description of central tendency.

Authors who use this formulation often speak of the choice function on A, but be advised that this is a slightly different notion of choice function.

This is to avoid the notion that a writing system that represents sounds must be either a syllabary or an alphabet, which implies that a system like Aramaic must be either a syllabary ( as argued by Gelb ) or an incomplete or deficient alphabet ( as most other writers have said ); rather, it is a different type.

He argues that this casts doubt on the notion that recessions are caused by a reallocation of resources from industrial production to consumption, since he argues that the Austrian business cycle theory implies that net investment should be below zero during recessions.

( Hume 1974: 322 ) In explaining how matters of fact are entirely a product of experience, he dismisses the notion that they may be arrived at through a priori reasoning.

In 1920, Thoralf Skolem simplified a previous result by Leopold Löwenheim, leading to the Löwenheim – Skolem theorem and, in 1930, to the notion of a Herbrand universe and a Herbrand interpretation that allowed ( un ) satisfiability of first-order formulas ( and hence the validity of a theorem ) to be reduced to ( potentially infinitely many ) propositional satisfiability problems.

It had been hoped that patient adherence to antipsychotics would be higher with the atypicals, but a 2008 review found that the data have failed to substantiate the notion that novel antipsychotic drug use leads to improved medication compliance and favorable clinical outcomes.

Indeed, naive set theory might be said to be based on this notion.

Even though the author of the book states that Ruth " just happens " to find Boaz's field ( Ruth 2: 3 ), the reader may be led to accede to the notion that in Bible terms there is no mere chance, but that chance and God's providence amount to the same thing.

After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870.

) She defined a generalized notion of " labels "— corresponding more or less to the full security markings one encounters on classified military documents, e. g., TOP SECRET WNINTEL TK DUMBO — that are attached to entities.

When Emil Post in his 1921 Introduction to a general theory of elementary propositions extended his proof of the consistency of the propositional calculus ( i. e. the logic ) beyond that of Principia Mathematica ( PM ) he observed that with respect to a generalized set of postulates ( i. e. axioms ) he would no longer be able to automatically invoke the notion of " contradiction " – such a notion might not be contained in the postulates:

Since the ordinary notion of consistency involves that of contradiction, which again involves negation, and since this function does not appear in general as a primitive in generalized set of postulates a new definition must be given ".

When fluxes are included the supersymmetry condition instead implies that the compactification manifold be a generalized Calabi – Yau, a notion introduced by.

Given a set S of matrices, each of which is diagonalizable, and any two of which commute, it is always possible to simultaneously diagonalize all of the elements of S. Equivalently, for any set S of mutually commuting semisimple linear transformations of a finite-dimensional vector space V there exists a basis of V consisting of simultaneous eigenvectors of all elements of S. Each of these common eigenvectors v ∈ V, defines a linear functional on the subalgebra U of End ( V ) generated by the set of endomorphisms S ; this functional is defined as the map which associates to each element of U its eigenvalue on the eigenvector v. This " generalized eigenvalue " is a prototype for the notion of a weight.

Thus weights are primarily of interest for abelian Lie algebras, where they reduce to the simple notion of a generalized eigenvalue for space of commuting linear transformations.

The primary notion of usability is that an object designed with a generalized users ' psychology and physiology in mind is, for example:

The notion of closure is generalized by Galois connection, and further by monads.

The language of fibre bundles allows this notion of a section to be generalized to the case when E is not necessarily a Cartesian product.

Finally, the notion of Gauss map can be generalized to an oriented submanifold X of dimension k in an oriented ambient Riemannian manifold M of dimension n. In that case, the Gauss map then goes from X to the set of tangent k-planes in the tangent bundle TM.

The differential of the argument is however globally defined ( except at the origin ), since differentiation only requires local data and different values of the argument differ by a constant, so the derivatives of different local definitions are equal ; this line of thought is generalized in the notion of covering spaces.

Ricci and Levi-Civita ( following ideas of Elwin Bruno Christoffel ) observed that the Christoffel symbols used to define the curvature could also provide a notion of differentiation which generalized the classical directional derivative of vector fields on a manifold.

Injective modules include divisible groups and are generalized by the notion of injective objects in category theory.

In the context of algebraic geometry, the notion of branch points can be generalized to mappings between arbitrary algebraic curves.

In linear algebra, quadratic polynomials can be generalized to the notion of a quadratic form on a vector space.

Nigel Hitchin introduced the notion of a generalized almost complex structure on the manifold M, which was elaborated in the doctoral dissertations of his students Marco Gualtieri and Gil Cavalcanti.

Although this term historically was derived from the notion of a ring ideal of abstract algebra, it has subsequently been generalized to a different notion.

A Thom isomorphism theorem for a homology theory is now accepted as the generalized notion of orientability for a homology theory.

More specifically, there is a general Poincaré duality theorem for generalized homology theories which requires a notion of orientation with respect to a homology theory, and is formulated in terms of a generalized Thom Isomorphism Theorem.

In a well defined sense it generalized the classical notion of minimal sufficient statistics from parametric statistics to arbitrary distributions, not necessarily of exponential form.