# irrational number

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Related to irrational number: imaginary number

## 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.

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.