different between incommensurable vs commensurable

incommensurable

English

Etymology

From Middle French incommensurable, from Medieval Latin incommensurabilis.

Pronunciation

  • (Received Pronunciation) IPA(key): /?nk??m?n?(?)??b?l/, /?nk??m?nsj????b?l/
  • (General American) IPA(key): /?n.k??m?n(t)s.??.b?l/, /?n.k??m?n(t)?.??.b?l/, /?n.k??m?n(t).s?.??.b?l/, /?n.k??m?n(t).??.??.b?l/

Adjective

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.
    The side and diagonal of a square are incommensurable with each other; the diameter and circumference of a circle are incommensurable.

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

  • incommensurate

Translations

Noun

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

  • incommensurable in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
  • incommensurable in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
  • incommensurable at OneLook Dictionary Search

French

Etymology

Borrowed from Late Latin incommens?r?bilis.

Pronunciation

  • IPA(key): /??.k?.m??.sy.?abl/

Adjective

incommensurable (plural incommensurables)

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

Derived terms

  • incommensurablement

Further reading

  • “incommensurable” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).

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commensurable

English

Etymology

Borrowed from Late Latin Latin commensurabilis (having a common measure) in 1550s, from Latin com- (with) + mensurabilis (measurable). Equivalent to com- +? mensurable.

Adjective

commensurable (comparative more commensurable, superlative most commensurable)

  1. Able to be measured using a common standard.
    A yard and a foot are commensurable, as both may be measured by inches.
  2. Related in size or scale; commensurate or proportionate.
  3. (mathematics) (of two or more numbers) Divisible by the same number WP
    The numbers 12 and 18 are commensurable, as both are divisible by 6, while 12 and 19 are incommensurable.

Antonyms

  • incommensurable

Translations


French

Adjective

commensurable (plural commensurables)

  1. (mathematics) commensurable

Synonyms

  • mesurable

commensurable From the web:

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  • what is commensurable with miles
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