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.

Jean Bodin, writing in the sixteenth century, may have been the seminal thinker, but it was the vastly influential John Austin who set out the main lines of the concept as now understood.

We will recall that the still confident liberals of the Truman administration gathered with other Western utopians in San Francisco to set up the legal framework, finally and at last, to rationalize war -- to rationalize want and fear -- out of the world: the United Nations.

And the best way to conceal and disguise the elements of an incest story is not to set out to write an incest story.

So when textbooks, like that of Baker set out drawings of the ' Ptolemaic System ', complete with earth in the center and the seven heavenly bodies epicyclically arranged on their several deferents, we have nothing but a misleading 20th-century idea of what never existed historically.

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.

The strongest appeal of the Copernican formulation consisted in just this: ideally, the justification for dealing with special problems in particular ways is completely set out in the basic ' rules ' of the theory.

You probably would not remember, since you never seemed to remember even the same moments as I, much less their intensity, one sunny midday on Fifth Avenue when you had set out with me for some final shopping less than a week before the wedding you staged for me with such reluctance at the Farm.

Even before the century was out the tide of reaction had set in.

We set up the Lloyd's Neck school, worked out its curriculum, and taught there.

It bulks under a veil of thin, new grass, like some embarrassing fact of physicalness, and I think Mrs. Pastern set out the statuary to soften its meaning.

A fire had just been lighted, he saw, and things had been set out for drinks, and, like any stray, his response to these comforts was instantaneous.

Hatless, in an overcoat of rough blue wool, I was given a proud farewell by my mother and father, and I set out into the strangely still streets of Brooklyn.

When they have 4 to 6 leaves and are thrifty little plants, it's time to set them out where they are to remain.

I started the seed in a flat in June and set out the little pansies in a cold frame.

Dr. Wilson C. Grant, of the Veterans' Administration Hospital, Coral Gables, Florida, and the University of Miami School of Medicine, set out to discover if avocados, because of their high content of unsaturated fatty acids, would reduce the cholesterol of the blood in selected patients.

To have applied statewide the decisions of the two cases heard in Superior Court, in my opinion, would have placed us clearly out of compliance with the Wagner-Peyser Act and would have immediately opened the way for the Secretary of Labor, were he so inclined, to notify the Governor of such noncompliance, set a date for hearing, and issue his finding.

A table or set of tables may be set out as in Table 2.1.

He set out on his 700-mile return journey with five families of discontented and disappointed Swiss who turned their eyes toward the United States.

He had enlisted in the Army straight out of high school and had immediately set about learning his new trade.

He set out to keep Troop H the best troop in the best regiment.

So Mel Chandler set out to sell him on the spirit of Garryowen, just as he himself had been sold a short time before.

This is in honor of John Ledyard, class of 1773, who scooped a canoe out of a handy tree and first set the course way back in his own student days.

Geely grunted and slid partly out, and Shayne's left arm snaked in around his neck to help him, while he set himself solidly on the roadway and swung his right fist to the big, gum-chewing jaw before Geely could straighten up.

Montero had set up a strong position, using every bale and box we had in addition to barricades of logs and brush.

Opposite every gate was a hitching post or a stone carriage-step, set with a rusty iron ring for tying a horse.

its mass of bright bloom set in a border of snow made my spirits rise every time I looked at it.

In the primary grades, reading permeates almost every aspect of school progress, and the children's early experiences of success or failure in learning to read often set a pattern of total achievement that is relatively enduring throughout the following years.

Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.

This is the principle which we will invoke in every case to set up a functional equation.

At the very moment that every attempt is being made to take management out from under the irrationality of anti-trust legislation, a drive is on to abolish collective bargaining under the guise of extending the anti-monopoly laws to unions who want no more than to continue to set wages in the same way that ship operators set freight rates.

A choice function is a function f, defined on a collection X of nonempty sets, such that for every set s in X, f ( s ) is an element of s. With this concept, the axiom can be stated:

This is not the most general situation of a Cartesian product of a family of sets, where a same set can occur more than once as a factor ; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all distinct sets in the family.

In the even simpler case of a collection of one set, a choice function just corresponds to an element, so this instance of the axiom of choice says that every nonempty set has an element ; this holds trivially.

Then our choice function can choose the least element of every set under our unusual ordering.

" The problem then becomes that of constructing a well-ordering, which turns out to require the axiom of choice for its existence ; every set can be well-ordered if and only if the axiom of choice holds.

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

** For every non-empty set S there is a binary operation defined on S that makes it a group.

** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.

That is, every consistent set of first-order sentences can be extended to a maximal consistent set.

For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬ AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets.