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From Middle French incommensurable, from Medieval Latin incommensurabilis.


  • IPA(key): /ɪnkəˈmɛnsjʊəɹəbəl/


incommensurable (comparative more incommensurable, superlative most incommensurable)

  1. (mathematics) Of two real numbers, such that their ratio is not a fraction of two integers.
  2. (arithmetics) Of two integers, having no common integer divisor except 1.
  3. Not able to be measured by the same standards as another term in the context; see measurement; contrast with unmeasurable or immeasurable, each of which means not able to be measured at all, the former more generally, the latter generally due to some infinite quality of the thing being described
    The side and diagonal of a square are incommensurable with each other; the diameter and circumference of a circle are incommensurable.

Related terms[edit]


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incommensurable (plural incommensurables)

  1. An incommensurable value or quantity; an irrational number.
    • 1946, Bertrand Russell, History of Western Philosophy, ch. 3:
      Unfortunately for Pythagoras, his theorem led at once to the discovery of incommensurables, which appeared to disprove his whole philosophy.

Further reading[edit]



incommensurable (plural incommensurables)

  1. incommensurable
  2. immeasurable

Further reading[edit]