irrational

[ih-rash-uh-nl]
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.
a.
(of a number) not capable of being expressed exactly as a ratio of two integers.
b.
(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.
a.
of or pertaining to a substitution in the normal metrical pattern, especially a long syllable for a short one.
b.
noting a foot or meter containing such a substitution.
noun
8.
Mathematics, irrational number.

Origin:
1425–75; late Middle English < Latin irratiōnālis. See ir-2, rational

irrationally, adverb
irrationalness, noun
nonirrational, adjective, noun
nonirrationally, adverb
nonirrationalness, noun


3. unreasonable, ridiculous; insensate.
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Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
irrational (ɪˈræʃənəl)
 
adj
1.  inconsistent with reason or logic; illogical; absurd
2.  incapable of reasoning
3.  maths
 a.  not rational
 b.  (as noun): an irrational
4.  in Greek or Latin verse prosody
 a.  of or relating to a metrical irregularity, usually the occurrence of a long syllable instead of a short one
 b.  denoting a metrical foot where such an irregularity occurs
 
ir'rationally
 
adv
 
ir'rationalness
 
n

Collins English Dictionary - Complete & Unabridged 10th Edition
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Etymonline
Word Origin & History

irrational
c.1470, "not endowed with reason" (of beats, etc.), from L. irrationalis "without reason," from in- "not" + rationalis "reason" (see reason). Meaning "illogical, absurd" is attested from 1641.
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Medical Dictionary

irrational ir·ra·tion·al (ĭ-rāsh'ə-nəl)
adj.
Not rational; marked by a lack of accord with reason or sound judgment.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
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Example sentences
Though seemingly irrational, this pattern of faculty politics is familiar to
  anyone who has worked in a university.
It seems irrational to feel the trees closing behind you, as if the forest is
  cutting you off from the present.
Bright's courage was almost as irrational as that of the rebels themselves.
It's time to rein in the irrational exuberance of those who raise political
  money.
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