# rational
## English
### Alternative forms

* rationall (obsolete)

### Pronunciation

* enPR: ră'sh(ə)nəl, IPA: /ˈɹæʃ(ə)nəl/
* Audio (US):(file)
* Audio (General Australian):(file)
* Rhymes: -æʃənəl

### Etymology 1

From Old French rationel, rational, from Latin rationalis (“of or belonging to reason, rational, reasonable; having a ratio”), from ratio (“reason; calculation”).

#### Adjective

rational (comparative more rational, superlative most rational)
* Capable of reasoning.
    Man is a rational creature.
** 2001, Mark Sainsbury, chapter 1, in Logical Forms — An Introduction to Philosophical Logic, 2nd edition, Blackwell Publishing, →ISBN, §7, page 32:The utility of valid arguments is a monument to our frailty: to the fact that we are not completely rational beings.
* Logically sound; not self-contradictory or otherwise absurd.
    His statements were quite rational.
** 1812 The Freethinking Christians' Magazine: Volume 2 p. 21
    Prevention for the future is now almost universally allowed to be the only rational plea for the infliction of punishment; but this, when left to the arbitrary discretion of individuals, always has been found, and always will be found, to degenerate into the exercise of revenge for the past.
* (of a person or personal characteristics) Healthy or balanced intellectually; exhibiting reasonableness.
    rational conduct
** 1867 C. Handfield Jones, Case Of Low Fever: Delirium: Incomplete Dementia. The British Medical Journal Vol. 2, No. 344, Aug. 3
    Temperature 99.8 degrees. Pulse 104. She was quite conscious and rational at times, at others very noisy.
** 2014 June 21, “Magician’s brain”, in The Economist, volume 411, number 8892:The [Isaac] Newton that emerges from the [unpublished] manuscripts is far from the popular image of a rational practitioner of cold and pure reason. The architect of modern science was himself not very modern. He was obsessed with alchemy.
* (mathematics, not comparable) Comprising, or expressible as, a ratio
** (arithmetic) Of a number, capable of being expressed as the ratio of two integers.
    ¾ is a rational number, but √2 is an irrational number.
** (algebra) Of an algebraic expression in indeterminates, or more generally a function: capable of being expressed as the ratio of two polynomials.
** (algebraic geometry) Of a variety: (informally) geometrically simple almost everywhere; (formally) birationally equivalent to projective space
** (algebraic geometry) Of a function between varieties: acting as a morphism on an open subset of its domain.
** (algebraic geometry) Of a point on an algebraic variety over a field: whose coordinates belong to the field in question (in contrast to those points of the variety which are only defined over the algebraic closure of the base field).
* (chemistry) Expressing the type, structure, relations, and reactions of a compound; graphic; said of formulae.
* (physics) Expressing a physical object.
    A rational table is physical, a written table is neither.

##### Antonyms

* (antonym(s) of “reasonable”): absurd, irrational, nonsensical, arbitrary
* (antonym(s) of “capable of reasoning”): arational, irrational, non-rational
* (antonym(s) of “number theory”): irrational

##### Derived terms

* antirational
* biorational
* birational
* contrarational
* extrarational
* hyperrational
* nonrational
* overrational
* prerational
* preterrational
* pseudorational
* Ratfor
* rational basis review
* rational choice theory
* rational dress
* rational egoism
* rational egoist
* rational function
* rational horizon
* rationalism
* rationalist
* rationalistic
* rationally
* rational numbers
* rational root theorem
* rational selfishness
* rational symptom
* semirational
* superrational
* transrational
* ultrarational
* unirational
* unrational

##### Related terms

* arational
* irrational
* non-rational
* rationale
* rationality
* rationalness
* subrational
* suprarational

##### Translations
#### Noun

rational (plural rationals)
* (mathematics) A rational number: a number that can be expressed as the quotient of two integers.
    The quotient of two rationals is again a rational.

##### Translations
### Etymology 2

From Old French rational, from Medieval Latin rationale (“a pontifical stole, a pallium, an ornament worn over the chasuble”), neuter of Latin rationalis (“rational”), for which see the first etymology. Translation of λογεῖον (logeîon) or perhaps λόγιον (lógion, “oracle”) in the Septuagint version of Exodus 28.

#### Noun

rational (plural rationals)
* (historical) The breastplate worn by Israelite high priests.
** 1609, The Holie Bible, […] (Douay–Rheims Bible), Doway: Lavrence Kellam, […], →OCLC, Exodvs 28:15, page 234:The Rationale of iudgement alſo thou shalt mke with embrodered worke of diuers colours, according to the workmanship of the Ephod of gold, hyacinth, and purple, and ſcarlet twiſe died, and twiſted ſilke.

##### Translations
### References

* “rational”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
* William Dwight Whitney, Benjamin E[li] Smith, editors (1911), “rational”, in The Century Dictionary […], New York, N.Y.: The Century Co., →OCLC.

### Further reading

* "rational" in Raymond Williams, Keywords (revised), 1983, Fontana Press, page 252.

### Anagrams

* notarial

## French
### Pronunciation

* Audio:(file)

### Noun

rational f (plural rationaux)
* rationale (religious clothing)

### Further reading

* “rational”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.

## German
### Etymology

Borrowed from Latin rationalis.

### Pronunciation

* IPA: [ˌʁat͡si̯oˈnaːl]
* Hyphenation: ra‧ti‧o‧nal
* Audio:(file)

### Adjective

rational (strong nominative masculine singular rationaler, comparative rationaler, superlative am rationalsten)
* rational

#### Declension
### Further reading

* “rational” in Duden online
* “rational” in Digitales Wörterbuch der deutschen Sprache