These are like the initial ways in which the world forces itself upon the self and thrusts the self into decision and choice.

The very nature of a choice so grounded in distinction and fact leads to the valid convictions which become force of will in the manifest leader.

Poster Products Inc., Chicago, Ill.: a changeable copy and display sign which consists of an extruded impact styrene background in choice of colors, onto which are mounted snap-in letters, figures, or words screened on acetate or other types of sheet stock.

They had been kind to us and we were indebted to them for one or two pleasant dinners, and for information as to where to shop, which dentist, doctor, plumber, and sitter to call ( not that there was much of a choice, since Catatonia was just a village ; ;

The problem arises, if it does arise, when the educator has to make a choice or a decision within the area of his professional competence, but which bears some relation to the social structure.

Instead, we became involved in a series of friendly, but overly formal, welcoming addresses to which we had no choice but to reply in kind.

It is obvious that the careful choice of photocathode which maximizes Af for a given input E ( in the case of the second stage, for the first phosphor screen emission ) is very important.

This would be by far the better choice, when `` it is a question of allowing the human race to survive, possibly under the domination of a regime which most of us detest, or of allowing it to destroy itself in appalling and prolonged anguish ''.

The latter represents a choice between any number of possible interpretations, none of which may have a standard agreed-upon meaning.

The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.

Thus the negation of the axiom of choice states that there exists a set of nonempty sets which has no choice function.

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

" 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.

For example, while the axiom of choice implies that there is a well-ordering of the real numbers, there are models of set theory with the axiom of choice in which no well-ordering of the reals is definable.

The axiom of choice produces these intangibles ( objects that are proven to exist, but which cannot be explicitly constructed ), which may conflict with some philosophical principles.

The debate is interesting enough, however, that it is considered of note when a theorem in ZFC ( ZF plus AC ) is logically equivalent ( with just the ZF axioms ) to the axiom of choice, and mathematicians look for results that require the axiom of choice to be false, though this type of deduction is less common than the type which requires the axiom of choice to be true.

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:

Each choice function on a collection X of nonempty sets is an element of the Cartesian product of the sets in X.

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.

The result is an explicit choice function: a function that takes the first box to the first element we chose, the second box to the second element we chose, and so on.

Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.

This gives us a definite choice of an element from each set, and makes it unnecessary to apply the axiom of choice.

If we try to choose an element from each set, then, because X is infinite, our choice procedure will never come to an end, and consequently, we will never be able to produce a choice function for all of X.

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

However, one can choose the index of the first element by an appropriate choice of the base address B.

The name choice for element 97 followed the previous tradition of the Californian group to draw an analogy between the newly discovered actinide and the lanthanide element positioned above it in the periodic table.

This means that the person involved should have legal capacity to give consent ; should be so situated as to be able to exercise free power of choice, without the intervention of any element of force, fraud, deceit, duress, over-reaching, or other ulterior form of constraint or coercion ; and should have sufficient knowledge and comprehension of the elements of the subject matter involved as to enable him / her to make an understanding and enlightened decision.

For the weighted mean of a list of data for which each element comes from a different probability distribution with known variance, one possible choice for the weights is given by:

Cautious choice and definition of characters thus is another important element in cladistic analyses.

The deliberate choice of scat syllables also is a key element in vocal jazz improvisation.

:“ even if the model its rational self-interest assumptions proves to be useful in explaining an important element of politics, it does not imply that all individuals act in accordance with the behavioral assumption made or that any one individual acts in this way at all times … the theory of collective choice can explain only some undetermined fraction of collective action.

It was able to deal with many kinds of errors and gave the user a choice to either remove the offending process and associated screen or allow the machine to show the Guru Meditation.

It was the second time the Country Party had effectively vetoed its senior partner's choice for the leadership ; in 1923 Earle Page had demanded that the Nationalist Party, one of the forerunners of the Liberals, remove Billy Hughes as leader before he would even consider coalition talks.

They can, however, become weeds in rock gardens, where they will often appear in the middle of choice, mat-forming alpine plants and can be difficult to remove.

The choice of Charles Cameron as Civil Commissioner in May 1801 did not remove these uncertainties, even though his presence assured the Maltese of the protection of the Empire.

But Jeremiah had been elected during the vacancy before Theobald's election, and the monks had not secured papal permission for the election of a new prior, so eventually Theobald decided to remove Jeremiah and install his own choice as prior.

In the given circumstances, the DAA had no choice but to remove the airbridges from the terminal design during construction of the new facility.

* If a single sink, toilet, or tub or shower drain is clogged the first choice is normally a drain cleaner that can remove soft obstructions such as hair and grease clogs that can accumulate close to interior drain openings.

* If more than one plumbing fixture is clogged the first choice is normally a drain cleaner that can remove soft or hard obstructions along the entire length of the drain, from the drain opening through the main sewer drain to the lateral piping outside the building.

The choice of the end where His-tag is added will depend mainly on the characteristics of the protein and the methods chosen to remove the tag.

Opponents say that this undermines individual freedom and personal responsibility, and worry that the state may be emboldened to remove more and more choice in the name of better population health overall.

During World War II the blue discharge became the discharge of choice for commanders seeking to remove homosexuals from the ranks.

EGD, or a compatible alternative such as prngd, gather pseudo-random entropy from various sources, process it to remove bias and improve cryptographic quality, and then make it available over a Unix domain socket ( with < tt >/ dev / egd-pool </ tt > being a common choice ), or over a TCP socket.

Once the female dog has been stabilized, then the treatment of choice is an emergency spay, to remove the infected organ, but as this prevents a female dog from breeding it is worth noting that some advances have been made in treating pyometra with long-term antibiotics and an agent to cause contraction of the uterus and expulsion of the pus.

Smith's wife, Elizabeth B. Watton, had paid $ 500 for the choice of plots, in Greenlawn Cemetery but had to remove the body to Crown Hill Cemetery in Indianapolis for fear of southern dissenters, the Sons of Liberty, desecrating his body and of local teens knocking over the markers.

The doctor has no choice but to call off the surgery: the creature has infiltrated Spock's spinal column with pieces of living tissue that are impossible to completely remove through surgery.

These people include consultant Fred Vorck, who advocates that consumers should have the choice to remove " integrated " features of Microsoft Windows and participates in the HFSLIP project ; Dino Nuhagic, who is the creator of nLite — a product that allows users to remove Windows components like Internet Explorer and Windows Media Player, amongst others ; and Shane Brooks, who created 98lite and XPLite to remove and manage Windows components after the installation of the operating system.

# Because of mutually assured destruction by a nuclear war, the Soviets had no choice but to bow to U. S. demands and remove the weapons.

Improper choice of a welding gas can lead to a porous and weak weld, or to excessive spatter ; the latter, while not affecting the weld itself, causes loss of productivity due to the labor needed to remove the scattered drops.

The choice of the type of amine will affect the required circulation rate of amine solution, the energy consumption for the regeneration and the ability to selectively remove either H < sub > 2 </ sub > S alone or CO < sub > 2 </ sub > alone if desired.