incommensurable

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English

Etymology

From Middle French incommensurable, from Medieval Latin incommensurabilis.

Its full etymology is equivalent to that of in- + commensurable.

Pronunciation

Adjective

incommensurable (comparative more incommensurable, superlative most incommensurable)

  1. (mathematics, of two real numbers) having a ratio that is not expressible as a fraction of two integers.
    The side and diagonal of a square are incommensurable with each other; the diameter and circumference of a circle are incommensurable.
  2. (mathematics, 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.

Usage notes

The term contrasts with unmeasurable and immeasurable in that both mean "not able to be measured at all", with the latter generally being because of some infinite quality of the thing being described.

Related terms

Translations

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Noun

incommensurable (plural incommensurables)

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

Further reading

French

Etymology

Borrowed from Late Latin incommēnsūrābilis.

Pronunciation

  • IPA(key): /ɛ̃.kɔ.mɑ̃.sy.ʁabl/
  • (file)

Adjective

incommensurable (plural incommensurables)

  1. (mathematics) incommensurable
  2. immeasurable
    Synonym: immense

Derived terms

Further reading