incommensurable

English

Etymology

From Middle French incommensurable, from Medieval Latin incommensurabilis.

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

Pronunciation

• (Received Pronunciation) IPA^(key): /ɪnkəˈmɛnʃ(ə)ɹəbəl/, /ɪnkəˈmɛnsjʊəɹəbəl/
• (General American) IPA^(key): /ɪn.kəˈmɛnt͡ʃ.ɹə.bəl/, /ɪn.kəˈmɛn(t).sə.ɹə.bəl/, /ɪn.kəˈmɛn(t).sə.ɹə.bəl/

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

• coprime
• incommensurate
• relatively prime

Translations

having no common divisor except 1

• Chinese:

  Mandarin: 互質／互质 (zh) (hùzhì), 互素 (zh) (hùsù)

• Czech: nesoudělný m
• Finnish: yhteistekijätön
• French: incommensurable (fr)
• Spanish: please add this translation if you can

not able to be measured by same standards

• Chinese:

  Mandarin: 缺乏可通约性

• Czech: nesouměřitelný (cs) m
• Dutch: incommensurabel (nl), onderling onmeetbaar
• Finnish: yhteismitaton
• French: sans commune mesure (fr), incommensurable (fr)
• Spanish: please add this translation if you can

The translations below need to be checked and inserted above into the appropriate translation tables. See instructions at Wiktionary:Entry layout § Translations.

Translations to be checked

• Swedish: ^{(please verify)} inkommensurabel (sv)

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

• “incommensurable”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
• “incommensurable”, in The Century Dictionary […], New York, N.Y.: The Century Co., 1911, →OCLC.
• “incommensurable”, in OneLook Dictionary Search.

French

Etymology

Borrowed from Late Latin incommēnsūrābilis.

Pronunciation

• IPA^(key): /ɛ̃.kɔ.mɑ̃.sy.ʁabl/

• Audio:

  (file)

Adjective

incommensurable (plural incommensurables)

1. (mathematics) incommensurable
2. immeasurable

   Synonym: immense

Derived terms

• incommensurablement

Further reading

• “incommensurable”, in Trésor de la langue française informatisé [Digitized Treasury of the French Language], 2012.