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From Latin irratiōnālis, from ir- + ratiōnālis.


  • enPR: ĭră'sh(ə)nəl, IPA(key): /ɪˈræʃ.(ə.)nəl/


irrational ‎(comparative more irrational, superlative most irrational)

  1. Not rational; unfounded or nonsensical.
    an irrational decision
    • July 18, 2012, Scott Tobias, AV Club The Dark Knight Rises[1]
      Where the Joker preys on our fears of random, irrational acts of terror, Bane has an all-consuming, dictatorial agenda that’s more stable and permanent, a New World Order that’s been planned out with the precision of a military coup.
  2. (mathematics, arithmetic, number theory, not comparable) Of a real number, that cannot be written as the ratio of two integers.
    The number π is irrational.



Derived terms[edit]


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irrational ‎(plural irrationals)

  1. A real number that can not be expressed as the quotient of two integers, an irrational number.
    • 1946, Bertrand Russell, History of Western Philosophy, I.24:
      The square root of 2, which was the first irrational to be discovered, was known to the early Pythagoreans, and ingenious methods of approximating to its value were discovered.