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Integral vs Rational - What's the difference?

integral | rational |

As an initialism integral

is (space|esa) (a satellite of the european space agency).

As an adjective rational is

capable of reasoning.

As a noun rational is

(mathematics) a rational number: a number that can be expressed as the quotient of two integers.

integral

English

Adjective

(en adjective)
  • Constituting a whole together with other parts or factors; not omittable or removable
  • * South
    • Ceasing to do evil, and doing good, are the two great integral parts that complete this duty.
  • (mathematics) Of, pertaining to, or being an integer.
  • (mathematics) Relating to integration.
  • (obsolete) whole; undamaged
  • * Francis Bacon
    • A local motion keepeth bodies integral .

    Synonyms

    * (constituting a whole) immanent, inherent, necessary

    Derived terms

    * integral brick * integral closure * integral cosmology * integral cuboid * integral current * integral curvature * integral curve * integral domain * integral drawing * integral ecology * integral element * integral energy * integral extension * integral fast reactor * integral field unit * integral function * integral geometry * integral graph * integral homology group * integral kernel * integral membrane protein * integral politics * integral polygedron * integral polynomial * integral post-metaphysics * integral psychology * integral transformative practice * integral yoga * integrity

    Related terms

    * integer

    Noun

    (wikipedia integral) (en noun)
  • (mathematics) A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.
    • The integral of x\mapsto x^2 on [0,1] is \frac{1}{3}.
  • (mathematics)
    • The integral of x^2 is \frac{x^3}{3} plus a constant.

    Synonyms

    * (limit of sums) definite integral * (antiderivative) antiderivative, indefinite integral,

    Antonyms

    * (antiderivative) derivative

    Derived terms

    * definite integral * half-integral * improper integral * indefinite integral * integral calculus * integral equation * integral theory * integral transform * integration * Riemann integral * Riemann-Stieltjes integral * Lebesgue integral

    Related terms

    * integer

    Anagrams

    * * * * English heteronyms ----

    rational

    English

    Alternative forms

    * rationall (obsolete)

    Etymology 1

    From (etyl) rationel, rational, from (etyl)

    Adjective

    (en adjective)
  • Capable of reasoning.
  • *
  • Logically sound; not contradictory or otherwise absurd.
  • (label) Healthy or balanced intellectually; exhibiting reasonableness.
  • *{{quote-magazine, date=2014-06-21, volume=411, issue=8892, magazine=(The Economist)
    • , title= Magician’s brain , passage=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.}}
  • 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, capable of being expressed as the ratio of two polynomials.
  • (label) Expressing the type, structure, relations, and reactions of a compound; graphic; said of formulae.
    • Antonyms
    * (reasonable) absurd, irrational, nonsensical * (capable of reasoning) arational, irrational, non-rational * (number theory) irrational
    Related terms
    * arational * irrational * non-rational * rationale * rationality * rationalness * subrational * suprarational

    Etymology 2

    From (etyl) rational, from , for which see the first etymology.

    Noun

    (en noun)
  • (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 .
  • A rational being.
    • (Young)

    References

    * *

    Anagrams

    *