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  2. Square root of 5 - Wikipedia

    en.wikipedia.org/wiki/Square_root_of_5

    It is more precisely called the principal square root of 5, to distinguish it from the negative number with the same property. This number appears in the fractional expression for the golden ratio. It can be denoted in surd form as . It is an irrational algebraic number. [1]

  3. Irrational number - Wikipedia

    en.wikipedia.org/wiki/Irrational_number

    The number √ 2 is irrational.. In mathematics, the irrational numbers (in-+ rational) are all the real numbers that are not rational numbers.That is, irrational numbers cannot be expressed as the ratio of two integers.

  4. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    All rational numbers are real, but the converse is not true. Irrational numbers (): Real numbers that are not rational. Imaginary numbers: Numbers that equal the product of a real number and the imaginary unit , where =. The number 0 is both real and imaginary.

  5. Category:Irrational numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Irrational_numbers

    In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a fraction a / b with a and b integers and b not zero. This is also known as being incommensurable, or without common measure. The irrational numbers are precisely those numbers whose expansion in any given base (decimal ...

  6. Real number - Wikipedia

    en.wikipedia.org/wiki/Real_number

    The real numbers include the rational numbers, such as the integer −5 and the fraction 4 / 3. The rest of the real numbers are called irrational numbers. Some irrational numbers (as well as all the rationals) are the root of a polynomial with integer coefficients, such as the square root √2 = 1.414...; these are called algebraic numbers.

  7. Rational number - Wikipedia

    en.wikipedia.org/wiki/Rational_number

    A real number that is not rational is called irrational. [5] Irrational numbers include the square root of 2 (⁠ ⁠), π, e, and the golden ratio (φ). Since the set of rational numbers is countable, and the set of real numbers is uncountable, almost all real numbers are irrational. [1]

  8. List of numbers - Wikipedia, the free encyclopedia

    en.wikipedia.org/wiki/List_of_numbers

    A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.

  9. Irrationality measure - Wikipedia

    en.wikipedia.org/wiki/Irrationality_measure

    Rational numbers have irrationality exponent 1, while (as a consequence of Dirichlet's approximation theorem) every irrational number has irrationality exponent at least 2. On the other hand, an application of Borel-Cantelli lemma shows that almost all numbers, including all algebraic irrational numbers , have an irrationality exponent exactly ...