It was Plummer, in fact, who coined the much quoted remark: `` Mr. Green indeed writes as if he had been present at the landing of the Saxons and had watched every step of their subsequent progress ''.

Even apart from the fact that now at the age of 31 my personal life is being totally disrupted for the second time for no very compelling reason -- I cannot help looking around at the black leather jacket brigades standing idly on the street corners and in the taverns of every American city and asking myself if our society has gone mad.

As a matter of fact you could probably find a new home development in every populated county in the country with three-bedroom ranch style cottages in the $14,000 range.

As a matter of fact, this happened every four or five months.

for, using the fact that N and N' commute Af and so when R is sufficiently large every term in this expression for Af will be 0.

But there is every reason to regard deal as a monosyllable, and because of the fact that /l/ commonly has the quality of AAb/ when it follows vowel sounds, deal seems to be a perfectly satisfactory rhyme with deal.

As `` a matter of fact no such complete solution of the dream has ever been accomplished in any case,, and what is more, every one attempting such solution has found that in most cases there have remained a great many components of the dream the source of which he has been unable to explain nor is the discussion closed on the subject of the mantic or prophetic power of dreams ''.

The fact that metropolitan churches of the major denominations have moved approximately every generation for the last hundred years becomes somewhat more intelligible in the light of this struggle to maintain economic balance.

Although he never gets to play while the clock is running, he gets a big kick -- several every Saturday, in fact -- out of football.

Almost every film bearing the imprimatur of Hollywood is physically authentic -- in fact, impeccably so.

The reason that we are able to choose least elements from subsets of the natural numbers is the fact that the natural numbers are well-ordered: every nonempty subset of the natural numbers has a unique least element under the natural ordering.

Thus, if every historian were to claim that there was a solar eclipse in the year 1600, then though we might at first naively regard that as in violation of natural laws, we'd come to accept it as a fact.

In point of fact, Capp maintained creative control over every stage of production for virtually the entire run of the strip.

However, despite those efforts, the presence of the Armed Forces on the border regions of the Brazilian Amazon continues to be sparse and disperse, given the fact that the Army has just 28 border detachments in that area, a total of 1, 600 soldiers, or 1 men for every of borders.

The company had re-leased estimates covering 20 % damage to be re-insured at minimal fees when in fact the damage was over 65 % and every claim was in the millions.

In fact, every compact metric space is a continuous image of the Cantor set.

This definition of cofinality relies on the axiom of choice, as it uses the fact that every non-empty set of cardinal numbers has a least member.

Bemba has publicly commented on election " irregularities ," despite the fact that every neutral observer has praised the elections.

Much encyclopaedism of the French Renaissance was based upon the notion of not including every fact known to humans, but only that knowledge that was necessary, where necessity was judged by a wide variety of criteria, leading to works of greatly varying sizes.

To Socrates, a person must become aware of every fact ( and its context ) relevant to his existence, if he wishes to attain self-knowledge.

In fact, every ESS corresponds to a Nash equilibrium, but some Nash equilibria are not ESSes.

In fact, every real n-dimensional vector space V is isomorphic to R < sup > n </ sup >.

Differences under the Maliki school included the fact that those following the Maliki school could state their purpose ( or niat ) once only for compulsory fasting which is valid for the whole month of Ramadhan whilst for the Shafi ' i. e. school ( see below ), one would have to state his purpose every day of the month of Ramadhan for his fast to be valid the next day.

Particles interact in every way available ; in fact, intermediate virtual particles are allowed to propagate faster than light.

In Fichte's technical terminology, the original unity of self-consciousness is to be understood as both an action and as the product of the same I, as a fact and / or act ( Tathandlung ), a unity that is presupposed by and contained within every fact and every act of empirical consciousness, though it never appears as such therein.

In 1870, Eduard Heine showed that a continuous function defined on a closed and bounded interval was in fact uniformly continuous.

In fact, a metric space is compact if and only if it is complete and totally bounded.

In fact, a bounded linear functional on C < sub > c </ sub >( X ) need not remain so if the locally convex topology on C < sub > c </ sub >( X ) is replaced by the supremum norm, the norm of C < sub > 0 </ sub >( X ).

We can also deduce from above that every positive linear functional is bounded, corresponding to the fact that the inner product is jointly continuous.

Although the campus is located in the city of Irvine, it is located very close to the city of Newport Beach ; in fact, the campus itself is directly bounded by the city of Newport Beach and Newport Coast on many sides.

More precisely, the Roche limit is determined by the fact that the function f, which can be regarded as a nonlinear measure of the force squeezing the ellipsoid towards a spherical shape, is bounded so that there is an eccentricity at which this contracting force becomes maximal.

The concept of bounded rationality revises this assumption to account for the fact that perfectly rational decisions are often not feasible in practice because of the finite computational resources available for making them.

Most geographers, in fact, do not look upon India as bounded by the river Indus, but add to it the four satrapies of the Gedrose, the Arachotë, the Aria, and the Paropamisadë, the River Cophes thus forming the extreme boundary of India.

The gross mis-measurement can be attributed to the fact that the property was bounded on three sides by water, and that neither the River nor the two creeks had regular shorelines.

The compactness of U ( n ) follows from the Heine – Borel theorem and the fact that it is a closed and bounded subset of M < sub > n </ sub >( C ).

A compact set in fact can be covered by finitely many balls of arbitrary small radius, because it is totally bounded.

The fact that U has dense range ensures it has a bounded inverse U < sup >− 1 </ sup >.

It is easy to verify that all examples above except the presheaf of bounded functions are in fact sheaves: in all cases the criterion of being a section of the presheaf is local in a sense that it is enough to verify it in an arbitrary neighbourhood of each point.

This is really a special case of a more general fact: Every continuous function from a compact space into a metric space is bounded.

One of the most important aspects of functions of bounded variation is that they form an algebra of discontinuous functions whose first derivative exists almost everywhere: due to this fact, they can and frequently are used to define generalized solutions of nonlinear problems involving functionals, ordinary and partial differential equations in mathematics, physics and engineering.

The Haar function system may on the one hand be preferable because of its wavelet properties ( e. g. localization ), on the other hand the Walsh functions are bounded ( in fact of modulus 1 everywhere ).

This fact can be used to show that, for any open set Ω ⊆ C, the set A ( Ω ) of all bounded, analytic functions u: Ω → C is a Banach space with respect to the supremum norm.

In fact, the closed graph theorem, the open mapping theorem and the bounded inverse theorem are all equivalent.

In fact, ≤ is also bounded complete.

The barycentric subdivision is chiefly used to replace an arbitrarily complicated convex polytope or topological cell complex by an assemblage of pieces, all of them of bounded complexity ( simplices, in fact ).

In fact, as was later shown by Banach, it is possible to define an " area " for all bounded subsets in the Euclidean plane ( as well as " length " on the real line ) such that congruent sets will have equal " area ".

Some analysis shows that, in fact, any two self-adjoint operators satisfying the above commutation relation cannot be both bounded.

The crucial fact here is that, for a bounded self adjoint operator T and a polynomial p,

He used the fact that is bounded on