# rational

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Related to Rationals: Radicals, Rational numbers, Real numbers

## ra·tion·al

(răsh′ə-nəl)
1. Having or exercising the ability to reason. See Synonyms at logical.
2. Consistent with or based on reason or good judgment; logical or sensible: rational decisions.
3. Of sound mind; sane: wondered if the eccentric neighbor was not completely rational.
4. Mathematics Capable of being expressed as a quotient of integers.
n. Mathematics
A rational number.

[Middle English racional, from Old French racionel, from Latin ratiōnālis, from ratiō, ratiōn-, reason; see reason.]

ra′tion·al·ness n.

## rational

(ˈræʃənəl)
1. using reason or logic in thinking out a problem
2. in accordance with the principles of logic or reason; reasonable
3. of sound mind; sane: the patient seemed quite rational.
4. endowed with the capacity to reason; capable of logical thought: man is a rational being.
5. (Mathematics) maths expressible as a ratio of two integers or polynomials: a rational number; a rational function.
n
(Mathematics) maths a rational number
[C14: from Latin ratiōnālis, from ratiō reason]
ˈrationalness n

## ra•tion•al

(ˈræʃ ə nl, ˈræʃ nl)

1. based on or agreeable to reason: a rational decision.
2. exercising reason: a rational negotiator.
3. sane; lucid: The patient seems rational.
4. Math.
a. capable of being expressed exactly by a ratio of two integers.
b. (of a function) capable of being expressed exactly by a ratio of two polynomials.
n.
[1350–1400; Middle English racional < Latin ratiōnālis=ratiōn- (s. of ratiō) reason + -ālis -al1]

## reasonable

rational
1. 'reasonable'

When someone is reasonable, they behave in a fair and sensible way.

Our mother was always very reasonable.
I can't do that, Morris. Be reasonable.

If something such as a proposal or judgement is reasonable, it is acceptable because it is fair or sensible.

Rules and procedures need to be accepted as reasonable by those who operate them.
There was no reasonable explanation for her decision.
2. 'rational'

You say that someone is rational when they are able to think clearly and make decisions and judgements based on reason rather than emotion.

You can also describe people's behaviour as rational.

This was a totally rational response to a set of complex problems.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 rational - an integer or a fractionrational numberreal, real number - any rational or irrational numberfraction - the quotient of two rational numbers Adj. 1 rational - consistent with or based on or using reason; "rational behavior"; "a process of rational inference"; "rational thought"logical - capable of or reflecting the capability for correct and valid reasoning; "a logical mind"reasonable, sensible - showing reason or sound judgment; "a sensible choice"; "a sensible person"sane - mentally healthy; free from mental disorder; "appears to be completely sane"irrational - not consistent with or using reason; "irrational fears"; "irrational animals" 2 rational - of or associated with or requiring the use of the mind; "intellectual problems"; "the triumph of the rational over the animal side of man"mental - involving the mind or an intellectual process; "mental images of happy times"; "mental calculations"; "in a terrible mental state"; "mental suffering"; "free from mental defects" 3 rational - capable of being expressed as a quotient of integers; "rational numbers"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangementirrational - real but not expressible as the quotient of two integers; "irrational numbers" 4 rational - having its source in or being guided by the intellect (as distinguished from experience or emotion); "a rational analysis"intellectual - appealing to or using the intellect; "satire is an intellectual weapon"; "intellectual workers engaged in creative literary or artistic or scientific labor"; "has tremendous intellectual sympathy for oppressed people"; "coldly intellectual"; "sort of the intellectual type"; "intellectual literature"

## rational

1. a rational decision
2. Man, as a rational being, may act against his impulses.
3. sane, balanced, normal, all there (informal), lucid, of sound mind, compos mentis (Latin), in your right mind Rachel looked calmer and more rational now.
sane

## rational

1. Able to reason validly:
2. Possessing, proceeding from, or exhibiting good judgment and prudence:
3. Mentally healthy:
Idioms: all there, in one's right mind, of sound mind .
4. Consistent with reason and intellect:
Translations
عاقِل، قادِر على التَّفْكيرعَقْلانِيّمَعْقول، مَنْطِقي
racionálnírozumnýrozumový
rationelfornuftig
järkeväjärkiperäinenrationaalinenjärjellinenjärkeenkäypä
racionalanrazboritrazuman
ésszerűracionális
skynsamlegurskynsamur; vitsmuna-

합리적인
protaujantisracionaliairacionalumasracionalus
domājošsloģiskssaprātīgs
rationell
ซึ่งมีเหตุผล
hợp lý

## rational

[ˈræʃənl]
1. (= logical) [argument, explanation] →
the rational thing to do would be tolo lógico or racional sería ...
2. (= reasonable) → razonable
3. (= sane) [person] →
he seemed quite rational
B. CPD rational number N (Math) →

## rational

[person] → rationnel(le)
[decision, explanation, argument] → rationnel(le); [solution] → rationnel(le); [thought, thinking, mind, reasoning] → rationnel(le)
(PSYCHOLOGY, PSYCHIATRY) (= of sound mind) → lucide

## rational

(= having reason) creature, personvernunftbegabt, rational
(= sensible, reasonable) person, action, thinking; activity, solution; (Med: = lucid, sane) person; it was the only rational thing to does war das einzig Vernünftige
(Math) → rational

## rational

[ˈræʃənl] adj (being) → razionale (Med) (lucid) → lucido/a; (faculty, action, argument) → razionale; (solution, explanation, reasoning) → logico/a, razionale

## rational

1. able to think, reason and judge etc. Man is a rational animal.
2. sensible; reasonable; logical; not (over-) influenced by emotions etc. There must be a rational explanation for those strange noises
ˌrationˈality noun

## rational

racionální rationel järkevä racionalan 理にかなった 합리적인 rationell ซึ่งมีเหตุผล hợp lý

## ra·tion·al

a. racional, cuerdo-a, basado-a en la razón.
References in periodicals archive ?
With an emphasis of proofs, this book explains concepts in advanced mathematics: the elements of logic, techniques of proof, elementary theory of sets, functions, relations, axiomatic theory of positive integers, elementary number theory, cardinality, counting techniques and combinatorics, and the construction of integers, rationals, and real and complex numbers.
For example, Artisans are likely interested in working with equipment and prefer to prove such skills over and over again; Idealists are likely to work well with people; Rationals are interested proving their skills working with systems.
Any value from Q, the set of nonnegative rationals, can be used as a time constant.
Let Q[y] be the set of rational functions in the variable y over the rationals Q and let [6.
The condition is easy to check, and we can find many rationals [t.
The organizing of Rapprochement and Human Harmony Week stems from the Islamic religion, as weell as Islamic and Arabic culture and civilization values that are rich in Equity, justice and constructive communication with all cultures and civilizations, considering that dialogue is the choice and approach of rationals and the most viable mean to solve problems and crisis that are facing contemporary human societies.
Here we seek a lagrangian that encompasses electrons, positrons, electromagnetism and gravity and seek to have equations that are polynomial rather than complicated rationals that arise from the operation of taking the inverse of the metric.
The idea was to articulate that a real number a intuitively is determined by the rationals smaller then a and those larger then a.
Topics follow the order of whole numbers, fractions, integers, rationals, and reals.
Although all real numbers can be defined as limits of infinite sequences of rationals, almost all of these numbers are noncomputable in the sense that they cannot be computed via any possible algorithm.
Extend Isabelle's computational features in direction of verfied Computer Algebra: simplification extended by algorithms beyond rewriting (cancellation of multivariate rationals, factorisation, partial fraction decomposition, etc), equation solving , integration, etc.

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