irrational number

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Related to Irrational numbers: Imaginary numbers

irrational number

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

Irrational Number

 

a number that is not rational (that is, not an integer or fraction). Real irrational numbers can be represented by an infinite non repeating decimal; for example, √2 = 1.41 …, π = 3.14 …. The existence of irrational ratios (for example, the irrationality of the ratio of the diagonal of a square to its side) was known in antiquity. The irrationality of the number π was established by the German mathematician J. Lambert (1766). However, a rigorous theory of irrational numbers was constructed only in the second half of the 19th century. Irrational numbers are divided into nonrational algebraic numbers and transcendental numbers.

irrational number

[i′rash·ən·əl ′nəm·bər]
(mathematics)
A number which is not the quotient of two integers.

irrational number

(mathematics)
A real number which is not a rational number, i.e. it is not the ratio of two integers.

The decimal expansion of an irrational is infinite but does not end in an infinite repeating sequence of digits.

Examples of irrational numbers are pi, e and the square root of two.
References in periodicals archive ?
The understanding that this is an irrational number was less secure, and would generally need some more explicit teaching in relation to sets of numbers and their properties).
In present work we don't state the task to find explicit form of irrational numbers fractal.
The Hindus also developed correct procedures for operating with irrational numbers.
or the concept of irrational number may be introduced.
Pi is an irrational number (a number which cannot be written as a finite or recurring sequence) but mathematically there are an infinite number of these, just as there are an infinite number of rational numbers.
Before they had access to being, these irrational numbers were already present in the epistemic domain of knowledge.
The 'evidence' that there are irrational numbers is (the proof of) the irrationality of [square root of 2]; the specification or identification of [square root of 2] as the distance-in-feet between the endpoints of sticks in my backyard has nothing to do with the closure of the rational field under [square root of x].
A particular class of irrational numbers is comprised of the quadratic surds, that is, all irrational numbers x which satisfy equations a[x.
Mark off a point as zero and then imagine the positive numbers marked off to the right and the negative numbers marked off to the left, with all the fractions and irrational numbers appropriately marked off between the whole numbers.
Beckett finds the Pythagorean struggle with irrational numbers emblematic.
241n): in fact, it was Cantor's purported definitions of higher-order real numbers, based upon iteration of his definition of irrational numbers, that met Dedekind's reservations.
Some theoretical topics, such as number representation, rational and irrational numbers and prime numbers are covered before diving back into historical events: Euclid, Diophantus, ancient codes and the origin of cryptography are all described.