It was all right to put a bunch of ranchers onto horses, to call them Night Riders, to set out to attack the largest mining combination the country had ever seen if all they wanted was adventure.

They recognized that slavery was a moral issue and not merely an economic interest, and that to recognize it explicitly in their Constitution would be in explosive contradiction to the concept of sovereignty they had set forth in the Declaration of 1776 that `` all men are created equal, that they are endowed by their Creator with certain unalienable rights, that among them are life, liberty and the pursuit of happiness.

We of the liberal-led world got all set for peace and rehabilitation.

The Axioms required to make the theoretical machinery operate are set out tersely and powerfully, so that all permissible operations within the theory can be traced rigorously back to these axioms, rules, and primitive notions.

For by now the original cause of the quarrel, Philip's seizure of Gascony, was only one strand in the spider web of French interests that overlay all western Europe and that had been so well and closely spun that the lightest movement could set it trembling from one end to the other.

He could produce carefully constructed orations, set and formal speeches, artfully and prayerfully made by writing and rewriting with all the aid his tutor and others could provide, and then delivered verbatim from memory.

In entering this union we will be surrendering most, if not all, of our economic autonomy to international bodies such as the Atlantic Institute ( recently set up ) or the O.E.C.D., I.M.F. and others.

The extent to which we can persuade the less developed countries to appraise their own resources, to set targets toward which they should be working, to establish in the light of this forward perspective the most urgent priorities for their immediate attention, and to do the other things which they must do to help themselves, all on a realistic long-term basis, will depend importantly on the incentives we place before them.

( For each State, make all computations set forth in items 1 to 8 above, and then add the results obtained for each State in item 8.

Before the Juniors entered the ring the Steward announced that after all Juniors had moved their dogs around the ring and set them up, they could relax with their dogs.

Above all, don't set up extravagant fringe benefits just to buy employee good will.

The huge market for changeable signs has spurred a universal demand for individual plastic letters, in all shapes and sizes -- and a number of companies are set up to supply them.

You can save all that shimming time if you set your windows in one, two, three order -- first the stud on one side, then the window, then the stud on the other side.

It was all set up so there would be no dust anywhere and so that their children would color in the coloring room, paint in the painting room, play with blocks in the block house, and do all the other things in the proper rooms at exactly the right time.

After all, if you were going to set up a workshop you had to have the proper equipment and that was that.

The set of all binomial distributions is called the family of binomial distributions, but in general discussions this expression is often shortened to `` the binomial distribution '', or even `` the binomial '' when the context is clear.

A unified set of regulations, applicable to all areas, was issued in 1929, and a complementary series of demographic inquiries in selected areas was instituted at the same time.

Unfortunately, however, and for reasons to be discussed in the following chapter, no rate relationships can be made completely nondiscriminatory as long as all or some of the rates must be set above marginal costs in order to yield adequate revenues.

J. Wheaton Smith, editor of the Warren Telegraph stated that `` the ends of justice must be satisfied, a solitary example must be set, in order that all those misnamed philantropists, who, actuated by a blind zeal, dare to instigate riot, treason, and murder, may heed it and shape their future course accordingly ''.

The set of all decisions is called the operating policy or, more simply, the policy.

The set of vectors Af constitutes the operating policy or, more briefly, the policy, and a policy is admissible if all the Af belong to S.

Houghton said 6 p.m. Friday had been set for a canvass of all 480 homes in the subdivision, which is located northeast of Dequindre and 14 Mile Road East.

The statement also points to a classic paradox: The more men turn toward God, who is not only in himself the paradigm of all unity but also the only ground on which human unity can ultimately be established, the more men splinter into groups and set themselves apart from one another.

# If V is a set of strings then V * is defined as the smallest superset of V that contains λ ( the empty string ) and is closed under the string concatenation operation.

Sets that can be assigned a Lebesgue measure are called Lebesgue measurable ; the measure of the Lebesgue measurable set A is denoted by λ ( A ).

# λ ( A ) ≥ 0 for every Lebesgue measurable set A.

# If A is a Lebesgue measurable set with λ ( A ) = 0 ( a null set ), then every subset of A is also a null set.

where B is a Borel set containing only the single eigenvalue λ < sub > i </ sub >.

The orientation of a particular set of sheets is identified by its three Miller indices ( h, k, l ), and let their spacing be noted by d. William Lawrence Bragg proposed a model in which the incoming X-rays are scattered specularly ( mirror-like ) from each plane ; from that assumption, X-rays scattered from adjacent planes will combine constructively ( constructive interference ) when the angle θ between the plane and the X-ray results in a path-length difference that is an integer multiple n of the X-ray wavelength λ.

where the sum is taken over all allocations of the set into λ ( unordered ) pairs.

The Woodward-Fieser rules, for instance, are a set of empirical observations used to predict λ < sub > max </ sub >, the wavelength of the most intense UV / Vis absorption, for conjugated organic compounds such as dienes and ketones.

The center of U ( n ) is the set of scalar matrices λI with λ ∈ U ( 1 ).

The value λ is called an eigenvalue of T and the set of all such eigenvalues is called the spectrum of T, denoted σ < sub > T </ sub >.

We now say that x ∈ V is an eigenvector of M if x is an eigenvector of T. Similarly, λ ∈ K is an eigenvalue of M if it is an eigenvalue of T and the spectrum of M, written σ < sub > M </ sub >, is the set of all such eigenvalues.

The spectrum of a bounded linear operator T acting on a Banach space X is the set of complex numbers λ such that λI − T does not have an inverse that is a bounded linear operator.

No notation is used to describe the set of all λ, which satisfy this condition, but for a subset: If λ-T does not have dense range but is injective, λ is said to be in the residual spectrum of T, denoted by σ < sub > r </ sub >( T ).

So the spectrum includes the set of approximate eigenvalues, which are those λ such that is not bounded below ; equivalently, it is the set of λ for which there is a sequence of unit vectors x < sub > 1 </ sub >, x < sub > 2 </ sub >, ... for which

The set of λ for which λI-T is injective but does not have dense range is known as the residual spectrum or compression spectrum of T and is denoted by σ < sub > r </ sub >( T ).

A complex number λ is said to be in the resolvent set, that is, the complement of the spectrum of a linear operator

Let B be a complex Banach algebra containing a unit e. Then we define the spectrum σ ( x ) ( or more explicitly σ < sub > B </ sub >( x )) of an element x of B to be the set of those complex numbers λ for which λe − x is not invertible in B.

He noticed that lines came in series and he found that he could simplify his calculations by using the wavenumber ( the number of waves occupying a set unit of length, equal to 1 / λ, the inverse of the wavelength ) as his unit of measurement.