irrational number

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Related to irrational number: imaginary number

irrational number

A real number that cannot be expressed as a ratio between two integers.

irrational number

(Mathematics) any real number that cannot be expressed as the ratio of two integers, such as π

irra′tional num′ber

a number that cannot be exactly expressed as a ratio of two integers.

ir·ra·tion·al number

A real number that cannot be expressed as a ratio between two integers. If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition. Pi and the square root of 2 (√2) are irrational numbers.
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.irrational number - a real number that cannot be expressed as a rational number
real, real number - any rational or irrational number
transcendental number - an irrational number that is not algebraic
algebraic number - root of an algebraic equation with rational coefficients
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References in periodicals archive ?
"We didn't want to set another irrational number," he says.
Mathematicians, for instance, provedlong ago that pi is an irrational number. This means that it takes a never-ending string of digits to express pi as a decimal number.
Instead, the irrational number, (1 + [square root of] 5)/2, pervades the pattern.
Pi represents an irrational number that begins with 3.141592653 and continues indefinitely.
Mathematicians everywhere will testify that Pi is a wonderful, never-ending irrational number which makes it the most fascinating number in world mathematics 3.1415926535 ..
Finite continued fractions represent always rational numbers, whereas infinite continued fractions represent irrational numbers. That is why any irrational number can be approximated by finite continued fractions--the convergents which deliver always the best and quickest approximation [11].
Coincidentally, the Carbondale sectional was held on "Pi Day," or March 14, so called because the first three numbers of the date are "3-14" like the irrational number pi (3.14).
In this section, we begin with an irrational number [[omega].sub.0] [member of] [0,1[ and a partition of [0,1] into l [less than or equal to] d subintervals with the requirement that one of the interior nodes is 1- [[omega].sub.0]:
Pi, the ratio of a circle's circumference to its diameter, is an irrational number that extends to trillions of digits beyond the decimal point.
In particular, an irrational number is a Liouville number if and only if it is not Diophantine.
They realised that [empty set] was an irrational number and embodied it in the pentagram, which they used as their secret sign.