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irrational

[ih-rash-uh-nl]
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adjective
  1. without the faculty of reason; deprived of reason.
  2. without or deprived of normal mental clarity or sound judgment.
  3. not in accordance with reason; utterly illogical: irrational arguments.
  4. not endowed with the faculty of reason: irrational animals.
  5. Mathematics.
    1. (of a number) not capable of being expressed exactly as a ratio of two integers.
    2. (of a function) not capable of being expressed exactly as a ratio of two polynomials.
  6. Algebra. (of an equation) having an unknown under a radical sign or, alternately, with a fractional exponent.
  7. Greek and Latin Prosody.
    1. of or relating to a substitution in the normal metrical pattern, especially a long syllable for a short one.
    2. noting a foot or meter containing such a substitution.
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noun
  1. Mathematics. irrational number.
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Origin of irrational

First recorded in 1425–75; late Middle English word from Latin word irratiōnālis. See ir-2, rational
Related formsir·ra·tion·al·ly, adverbir·ra·tion·al·ness, nounnon·ir·ra·tion·al, adjective, nounnon·ir·ra·tion·al·ly, adverbnon·ir·ra·tion·al·ness, noun

Synonyms

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3. unreasonable, ridiculous; insensate.
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

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British Dictionary definitions for irrationally

irrational

adjective
  1. inconsistent with reason or logic; illogical; absurd
  2. incapable of reasoning
  3. maths
    1. not rational
    2. (as noun)an irrational
  4. prosody (in Greek or Latin verse)
    1. of or relating to a metrical irregularity, usually the occurrence of a long syllable instead of a short one
    2. denoting a metrical foot where such an irregularity occurs
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Derived Formsirrationally, adverbirrationalness, noun
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Word Origin and History for irrationally

irrational

adj.

late 15c., "not endowed with reason" (of beats, etc.); earlier (of quantities) "inexpressible in ordinary numbers" (late 14c.); from Latin irrationalis "without reason," from assimilated form of in- "not, opposite of" (see in- (1)) + rationalis "reason" (see rational). Meaning "illogical, absurd" is attested from 1640s. Related: Irrationally.

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Online Etymology Dictionary, © 2010 Douglas Harper

irrationally in Medicine

irrational

(ĭ-răshə-nəl)
adj.
  1. Not rational; marked by a lack of accord with reason or sound judgment.
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The American Heritage® Stedman's Medical Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.