noun
definition
A rational number: a number that can be expressed as the quotient of two integers.
example
The quotient of two rationals is again a rational.
adjective
definition
Capable of reasoning.
example
Man is a rational creature.
definition
Logically sound; not contradictory or otherwise absurd.
example
His statements were quite rational.
definition
(of a person or personal characteristics) Healthy or balanced intellectually; exhibiting reasonableness.
example
rational conduct
definition
Of a number, capable of being expressed as the ratio of two integers.
example
¾ is a rational number, but √2 is an irrational number.
definition
Of an algebraic expression, capable of being expressed as the ratio of two polynomials.
definition
Expressing the type, structure, relations, and reactions of a compound; graphic; said of formulae.
definition
Expressing a physical object.
example
A rational table is physical, a written table is neither.
Examples of rational in a Sentence
The gut wrenching pain left him unable to process any rational thought.
It is not exactly an attempt to base Christian faith on rational scepticism.
Rational system is the first and last word in this philosophy.
Nevertheless, ants can teach " rational beings " many valuable lessons.
Once the shock wore off, rational thinking set in and he calmed down, feeling this might be an advantage.
There must be a God, who could compel irrational matter to serve rational ends - so ran the old argument.
The good man is the perfectly rational or perfect self-consistent man; and that is a full account of virtue, though Kant professes to re-interpret it still further in a much more positive sense as implying the service of humanity.
Where rational cultivation has been introduced, it has almost always been by non-Sardinian capitalists.
The possibility of reforming these contracts in some parts of the kingdom has been studied, in the hope of bringing them into closer harmony with the needs of rational cultivation and the exigencies of social justice.
These physical discomforts rendered rational thought and remembrance near impossible.
The critics of Aquinas - Duns Scotus and the later Nominalists - show some tendency towards rational scepticism.
In fact no rational cosmology is possible.
For myself, I think utter agnosticism is the most rational of starts.
To Bolkonski so many people appeared contemptible and insignificant creatures, and he so longed to find in someone the living ideal of that perfection toward which he strove, that he readily believed that in Speranski he had found this ideal of a perfectly rational and virtuous man.
In Prince Andrew's eyes Speranski was the man he would himself have wished to be--one who explained all the facts of life reasonably, considered important only what was rational, and was capable of applying the standard of reason to everything.
I too wondered about my wife's rational.
Holiness, " the perfect accordance of the will with the moral law," demands an endless progress; and " this endless progress is only possible on the supposition of an endless duration of the existence and personality of the same rational being (which is called the immortality of the soul)."
During 1906 a more rational view of the value of immigration was adopted by the various state governments and by the federal government, and immigration to Australia is now systematically encouraged.
The Rational Psychology formulates immortality on the ground that the immaterial soul has no parts to suffer decay - the argument which Kant's Critique of Pure Reason " refutes" with special reference to the statement of it by Moses Mendelssohn.
The formative principle or force of the world is said to contain the several rational germinal forms of things.
The whole world is represented by the figure of a tree, of which the seeds and roots are the first indeterminate matter, the leaves the accidents, the twigs and branches corruptible creatures, the blossoms the rational soul, and the fruit pure spirits or angels.
If Maimonides represented Judaism on its rational side, Rashi was the expression of its traditions.
Rational formulae of a much simpler description than these graphic formulae are generally employed.
He replenished the treasury by a more equable and rational system of assessing and collecting the taxes.
The six short Satires of Persius (34-62) are the purest product of Stoicism - a Stoicism that had found in a contemporary, Thrasea, a more rational and practical hero than Cato.
He taught that the Bible contained the elements not only of true religion but also of all rational philosophy.
Hugh James Rose had published in England (1825) a volume of sermons on the rationalist movement (The State of the Protestant Religion in Germany), in which he classed Bretschneider with the rationalists; and Bretschneider contended that he himself was not a rationalist in the ordinary sense of the term, but a "rational supernaturalist."
And it is easy to see how from this position Schelling was led on to the further statements that not in the rational conception of God is an explanation of existence to be found, nay, that all rational conception extends but to the form, and touches not the real - that God is to be conceived as act, as will, as something over and above the rational conception of the divine.
The confusion already alluded to between "pure" and "rational" hedonism is nowhere more clearly exemplified than in the misconceptions which have arisen as to the doctrine of the Epicureans.
The true hedonist will aim at a life of enduring rational happiness; pleasure is the end of life, but true pleasure can be obtained only under the guidance of reason.
Its adherents were recruited on the one hand from the old gnostic sects (especially from the Marcionites - Manichaeism exerted besides this a strong influence on the development of the Marcionite churches of the 4th century), on the other hand from the large number of the "cultured," who were striving after a "rational" and yet in some manner Christian religion.
If this be applied to the right-hand side of the identity m m m 2 m2 tan-=- - n n -3n-5n" it follows that the tangent of every arc commensurable with the radius is irrational, so that, as a particular case, an arc of 45 having its tangent rational, must be incommensurable with the radius; that is to say, 3r/4 is an incommensurable number."
In 1873 Charles Hermite proved that the base of the Napierian logarithms cannot be a root of a rational algebraical equation of any degree.3 To prove the same proposition regarding 7r is to prove that a Euclidean construction for circle-quadrature is impossible.
For in such a construction every point of the figure is obtained by the intersection of two straight lines, a straight line and a circle, or two circles; and as this implies that, when a unit of length is introduced, numbers employed, and the problem transformed into one of algebraic geometry, the equations to be solved can only be of the first or second degree, it follows that the equation to which we must be finally led is a rational equation of even degree.
The soul is partly irrational, partly rational; and therefore there are two kinds of virtue.
As the rational is either deliberative or scientific, either practical or speculative intellect, there are two virtues of the intellect - prudence of the deliberative or practical, and wisdom of the scientific or speculative, intellect.
No doubt, rational evidences had appeared in books of rhetoric, as we see from Plato's Phaedrus, 266-267,where we find proofs,probabilities, refutation and maxim, but mixed up with other evidences.
The point of Aristotle was to draw a line between rational and other evidences, to insist on the former, and in fact to found a logic of rhetoric. But if in the Rhetoric to Alexander, not he, but Anaximenes, had already performed this great achievement, Aristotle would have been the meanest of mankind; for the logic of rhetoric would have been really the work of Anaximenes the sophist, but falsely claimed by Aristotle the philosopher.
In an ascending scale, a plant is an organism with a nutritive soul; an animal is a higher organism with a nutritive, sensitive, orectic and locomotive soul; a man is the highest organism with a nutritive, sensitive, orectic, locomotive and rational soul.
The existence of physical evil, and still more of moral evil, forbids the assumption without qualification that the real is the rational.
As usual, the excessive self-introspection was not checked by a rational criticism; the individual was guided by his own reason, the limitations of which he did not realize; and in becoming a law unto himself he ignored the accumulated experiences of civilized humanity.'
If m and n are finite cardinal numbers, the rational number m/n is the relation which any finite cardinal number x bears to any finite cardinal number y when n X x = m X y.
Thus the rational number one, which we will denote by ' r, is not the cardinal number I; for t r is the relation I/I as defined above, and is thus a relation holding between certain pairs of cardinals.
Similarly, the other rational integers must be distinguished from the corresponding cardinals.
The arithmetic of rational numbers is now established by means of appropriate definitions, which indicate the entities meant by the operations of addition and multiplication.
A real number is a class (a, say) of rational numbers which satisfies the condition that it is the same as the class of those rationals each of which precedes at least one member of a.
Similarly, any rational real number is distinct from the corresponding rational number.
This is exactly the same reason as that which has led mathematicians to work with signed real numbers in preference to real numbers, and with real numbers in preference to rational numbers.
Note that classes are here required in extension, so that the class of human beings and the class of rational featherless bipeds are identical; similarly for relations, which are to be determined by the entities related.
The compactness of the series of rational numbers is consistent with quasi-gaps in it - that is, with the possible absence of limits to classes in it.