Definition of irrational in English:


Line breaks: ir|ration¦al
Pronunciation: /ɪˈraʃ(ə)n(ə)l


  • 2 Mathematics (Of a number, quantity, or expression) not expressible as a ratio of two integers, and having an infinite and non-recurring expansion when expressed as a decimal. Examples of irrational numbers are the number π and the square root of 2.
    More example sentences
    • What about a seed angle derived from the golden ratio, an irrational number?
    • The square root of 2 is an irrational number because it can't be written as a ratio of two integers.
    • How can mathematical concepts like points, infinitesimally small quantities, or irrational numbers be anything but products of our minds?


Mathematics Back to top  
  • An irrational number or quantity; a surd.
    More example sentences
    • Eudoxus's definition of equal ratios corresponds exactly to the modern theory of irrationals.
    • Whether such quirks in the irregularity of irrationals have any implications for number theory remains an open question for mathematicians.
    • His commentary to Euclid is of interest because of its discussion of unordered irrationals.



Pronunciation: /-ˈnalɪti/
More example sentences
  • The bitterness and irrationality of the thought frightened me, and I did my best to push it away.
  • It would seem that the accused also has to accept his victim's phobias, irrationality or stupidity.
  • The ending of the film suggests that rationality and irrationality are interchangeable and not very far apart from one another.


(also irrationalise) verb
More example sentences
  • When one thinks of planar travel the mind can often be boggled, confused, deceived and irrationalized.
  • The absence of knowledge affects human behaviour by reducing, distorting, and irrationalising the choices made by individuals.
  • I have reason to believe that she is about to irrationalize thinking on every issue.


More example sentences
  • I felt quite irrationally pleased with myself, as though I had actually achieved something.
  • Funny how perfectly rational people behave irrationally in times of war.
  • He is at times inspiringly Japanese, then suddenly, completely and irrationally unconventional.


late Middle English: from Latin irrationalis, from in- 'not' + rationalis (see rational).

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Pronunciation: ˌkələrəˈto͝orə
elaborate ornamentation of a vocal melody