noun

definition

A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.

definition

A subring closed under multiplication by its containing ring.

definition

(lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).

definition

A collection of sets, considered small or negligible, such that every subset of each member and the union of any two members are also members of the collection.

definition

(Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍.

Examples of ideals in a Sentence

You love your country's ideals, goals, values, and aspirations.

Different ideals dominate the party in the different states.

Surely we shall all find at last the ideals we are seeking....

Then came the work in college--original theme writing with new ideals of composition or at least new methods of suggesting those ideals.

It is a problem for empiricism; given a world where nothing but phenomenal sequences exist, to account for moral ideals.

Certainly no measure marked more clearly the abandonment of democratic ideals.

Amid all the ceremonialism of its priesthood there were also high ideals set forth in Zoroastrian religion of what a priest should be.

The succeeding age was an age of unmitigated egoism, growing in which the old ideals were abandoned and the old corruption examples were forgotten.

A close and somewhat strange intimacy, considering the difference in the characters and ideals of the two men, between Laud and Buckingham now began, and proved the chief instrument of Laud's advancement.

Upon its promulgation it speedily became the book which both gave the religious ideals of the age, and moulded the phraseology in which these ideals were expressed.

They held up before a backsliding people the ideals of human duty, of religious truth and of national policy.

Man should worship them, but his worship is the reverence due to the ideals of perfect blessedness; it ought not to be inspired either by hope or by fear.

The time had, indeed, not yet come to attempt any conspicuous breach with the constitutional principle; but the new ministry was such as the imperial sentiment would approve, inimical to the German ideals of Frankfort, devoted to the traditions of the Habsburg monarchy.

The quick reaction and sharp criticism of unfortunate acts and decisions indicated that free speech and free press were still basic ideals in the United States.

Young, emotional, impressionable, well-meaning and egotistic, Alexander displayed from the first an intention of playing a great part on the world's stage, and plunged with all the ardour of youth into the task of realizing his political ideals.

Yet the document is of great interest, as in it we find formulated for the first time in an official despatch those exalted ideals of international policy which were to play so conspicuous a part in the affairs of the world at the close of the revolutionary epoch, and issued at the end of the 10th century in the Rescript of Nicholas II.'

The brilliant promise of his early years; the haunting memory of the crime by which he had obtained the power to realize his ideals; and, in the end, the terrible ' Apercu des idees de l'Empereur, Martens IV.

The Book of Discipline and the Book of Common Order express Knox's ideals, which, as far as they were noble, as in the matter of education and of provision for the poor, remained, in part or in whole, " devout imaginations."

These, however, were already outworn forms, lingering on in a period which had chosen other ideals.

The excesses of John of Leiden, the Brigham Young of that age, cast an unjust stigma on the Baptists, of whom the vast majority were good, quiet people who merely carried out in practice the early Christian ideals of which their persecutors prated.

It is the prose epic of feudalism, and its romantic spirit, its high ideals, its fantastic gallantry, its ingenious adventures, its mechanism of symbolic wonders, and its flowing style have entranced readers of such various types as Francis I.

It is evil desires, low ideals, useless cravings, idle excitements, that are to be suppressed by the cultivation of the opposite of right desires, lofty aspirations.

Between this drama and its successor, Die Brazil von Messina, Schiller translated and adapted to his classic ideals Shakespeare's Macbeth (1801) and Gozzi's Turandot (1802).

The limitations of the test were the limitations of the educational and philosophic ideals of the time, in which a dogmatic basis was presupposed to all knowledge and criticism was limited to the superstructure.

In 1836 he founded the Dublin Review, partly to infuse into the lethargic English Catholics higher ideals of their own religion and some enthusiasm for the papacy, and partly to enable him to deal with the progress of the Oxford Movement, in which he was keenly interested.

But increasing culture presents new ideals, and the mind, absorbing the ethical spirit of its environment, gradually emancipates itself from conventions and superstitions.

The latter supplied only the rough materials; the Gotz von Berlichingen whom Goethe drew, with his lofty ideals of right and wrong, and his enthusiasm for freedom, is a very different personage from the unscrupulous robber-knight of the 16th century, the rough friend of Franz von Sickingen and of the revolting peasants.

As Friederike had fitted into the background of Goethe's Strassburg life, Lotte into that of Wetzlar, and Lili into the gaieties of Frankfort, so now Charlotte von Stein, the wife of a Weimar official, was the personification of the more aristocratic ideals of Weimar society.

Again, in Winckelmann and seine Zeit (1805) Goethe vigorously defended the classical ideals of which Winckelmann had been the founder.

With the aid of the vast body of Faust literature which has sprung up in recent years, and the many new documents bearing on its history above all, the so-called Urfaust, to which reference has already been made - we are able now to ascribe to their various periods the component parts of the work; it is possible to discriminate between the Sturm and Drang hero of the opening scenes and of the Gretchen tragedy - the contemporary of Gotz and Clavigo and the superimposed Faust of calmer moral and intellectual ideals - a Faust who corresponds to Hermann and Wilhelm Meister.

His object is to protest against the growing secularization of the Pharisaic party through its adoption of popular Messianic beliefs and political ideals.

There are moreover many traces of conflicting ideas and ideals, of cruder beliefs and customs, and of attempts to remove or elevate them.

It is in keeping with the old conceptions of the divine kingship, which, though they survive only in isolated biblical references, live on in the ideals of the Messianic king and his kingdom and in the post-exilic high priest. ?

While the code, according to its own lights, aims at strict justice rather than charity, the Old Testa ment has reforming aims, and the religious, legislative and social ideals are characterized by the insistence upon a lofty moral and ethical standard.

These ideals are more religious than democratic.

On literary-historical grounds the Pentateuch in its present form is post-exilic, posterior to the old monarchies and to the ideals of the earlier prophetical writings.

Moreover, Jefferson's ideals were high; his reasons for changes were in general excellent; he at least so far resisted the great pressure for office - producing by his resistance dissatisfaction within his party - as not to have lowered, apparently, the personnel of the service; and there were no such blots on his administration as President Adams's "midnight judges."

The Eastern Question, though its roots are set far back in history - in the ancient contest between the political and intellectual ideals of Greece and Asia, and in the perennial rivalry of the powers for the control of the great trade routes to the East - dates in its modern sense from the treaty of Kuchuk Kainarji in 1774, which marked the definitive establishment of Russia as a Black Sea power and formed the basis of her special claims to interfere in the affairs of the Ottoman empire.

The renewal of an aggressive policy thus announced to the world soon produced a new crisis in the Eastern Question, which had meanwhile become complicated by the growth of Pan-Slav ideals in eastern Europe.

The reality of mathematics, equally with that of the ideals of morals drawn from within, does not extend to the " ectypes " of the outer world.

Out of these developed, by the labours of the prophets, a religion of high spirituality and exalted ethical ideals.

In the Old Testament repeatedly they are found in conflict with the prophetic ideals.

With the revival of civilized conditions in secular life, secular ideals in art also revived; the ecclesiastical traditions in painting and sculpture, which always tend to become stereotyped, began in the West to be encroached upon long before the period of the "Renaissance."

They struck upon the unfortunate and opprobrious term "middle ages" for that which stood between them and their classic ideals.

St Norbert was a friend of St Bernard of Clairvaux - and he was largely influenced by the Cistercian ideals as to both the manner of life and the government of his order.

This admirable body represents a significant departure from medieval ideals.

Not that medieval ideals were by any means dead; they never burned more brightly than in the Spain of St Teresa (1515-82).

The unity of doctrine, liturgy and moral ideals is preserved by an intimate union with the see of Rome.

Both, too, were spiritual and elastic tendencies toward progress, ideals rather than solid organisms.

Yet no other treatment was possible upon the lines laid down at the outset, where it was explained why the term Renaissance cannot now be confined to the Revival of Learning and the effect of antique studies upon literary and artistic ideals.

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