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irrational

irrational

3 7.8
A number that cannot be written as a fraction
  • adjective
  • /ɪˈræʃənl/
  • Specialized
translation icon : irracional
  • Now there is an irrational number that is the most irrational number, by which I mean it can't be approximated by fractions very well.
  • irrational number
  • rational and irrational

Maybe a Nash equilibrium is comprised of irrational numbers, which I cannot specify.

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Examples

  • OK, so and the one of the features about irrational numbers is that they're decimal expansion because they're not a quotient of two whole numbers.

  • Numbers like pi and e are classified as irrational because they cannot be written as the ratio of two integers.

  • Then we're going to have two real irrational roots.

  • So that's going to be two real irrational numbers.

  • Because pi is an "irrational" number, you can't represent it as a fraction made up of two whole numbers.

    Academic text (2004)
  • Irrational numbers opened the door to the baroque world of the Mandelbrot set.

    Academic text (2004)
  • Cantor showed that the irrational numbers outnumber the rational ones by a factor of roughly infinity.

    Blog text (15)
  • The square root of 2 is an example of an irrational number, as it cannot be expressed as a fraction.

  • An irrational number cannot be represented exactly as a simple fraction, such as 1/3 or 4/5.

Antonyms

rational
  • Specialized
3 7.4

Expressible as a fraction of two whole numbers

Compounds

irrational number
  • Specialized
1 5.6

A number that cannot be written as a fraction, for example π or √2

A strong dislike of a person or group without good reason

A sudden strong wish to do something without a clear reason

A reason for doing something that is not logical or sensible

Surface Forms

irrational positive

Morphology

irrational = rational (semi-transparent) = ir + rational

Morphologically regular (ir- + rational) but the mathematical sense of 'rational' is specialized; learners who only know the everyday 'reasonable' sense may not infer the numeric meaning.

Etymology

Irrational comes from the Latin parts ir- 'not' and ratio 'a relationship of numbers' or 'a fraction'. So in math an irrational number is 'not a ratio' and cannot be written as a simple fraction, as with Pi.