rational
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rational¹
- /ˈɹæʃ(ə)nəl/
Rhymes with -æʃənəl
Where it comes from
From Old French rationel, rational, from Latin rationalis (“of or belonging to reason, rational, reasonable; having a ratio”), from ratio (“reason; calculation”).
adjective more rational · most rational · rationall
- Capable of reasoning. Man is a rational creature.
- Behaving according to some partial order of preferences.
- Logically sound; not self-contradictory or otherwise absurd. His statements were quite rational.
- Healthy or balanced intellectually; exhibiting reasonableness. rational conduct
- Of a number, capable of being expressed as the ratio of two integers. ¾ is a rational number, but √2 is an irrational number.
- Of an algebraic expression in indeterminates, or more generally a function: capable of being expressed as the ratio of two polynomials.
- Of a variety: (informally) geometrically simple almost everywhere; (formally) birationally equivalent to projective space
- Of a function between varieties: acting as a morphism on an open subset of its domain.
- 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).
- synonymous replacement for "condensed" in condensed formula.
noun rationals · rationall
- A rational number: a number that can be expressed as the quotient of two integers. The quotient of two rationals is again a rational.
rational²
- /ˈɹæʃ(ə)nəl/
Rhymes with -æʃənəl
Where it comes from
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 rationals · rationall
- The breastplate worn by Israelite high priests. 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.
