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  2. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Rational numbers (): Numbers that can be expressed as a ratio of an integer to a non-zero integer. [3] All integers are rational, but there are rational numbers that are not integers, such as −2/9. Real numbers (): Numbers that correspond to points along a line. They can be positive, negative, or zero.

  3. Rational number - Wikipedia

    en.wikipedia.org/wiki/Rational_number

    The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational coefficients, although the term ...

  4. Integer - Wikipedia

    en.wikipedia.org/wiki/Integer

    For example, 21, 4, 0, and −2048 are integers, while 9.75, ⁠5 + 1 / 2 ⁠, 5/4, and √ 2 are not. [8] The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers.

  5. Irrational number - Wikipedia

    en.wikipedia.org/wiki/Irrational_number

    Examples are e r and π r, which are transcendental for all nonzero rational r. Because the algebraic numbers form a subfield of the real numbers, many irrational real numbers can be constructed by combining transcendental and algebraic numbers. For example, 3 π + 2, π + √ 2 and e √ 3 are irrational (and even transcendental).

  6. Non-integer base of numeration - Wikipedia

    en.wikipedia.org/wiki/Non-integer_base_of_numeration

    The numbers d i are non-negative integers less than β. This is also known as a β-expansion, a notion introduced by Rényi (1957) and first studied in detail by Parry (1960). Every real number has at least one (possibly infinite) β-expansion. The set of all β-expansions that have a finite representation is a subset of the ring Z[β, β −1].

  7. Algebraic number - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number

    The name algebraic integer comes from the fact that the only rational numbers that are algebraic integers are the integers, and because the algebraic integers in any number field are in many ways analogous to the integers. If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O K.

  8. Number - Wikipedia

    en.wikipedia.org/wiki/Number

    Fractions are written as two integers, the numerator and the denominator, with a dividing bar between them. The fraction ⁠ m / n ⁠ represents m parts of a whole divided into n equal parts. Two different fractions may correspond to the same rational number; for example ⁠ 1 / 2 ⁠ and ⁠ 2 / 4 ⁠ are equal, that is:

  9. p-adic number - Wikipedia

    en.wikipedia.org/wiki/P-adic_number

    The 3-adic integers, with selected corresponding characters on their Pontryagin dual group. In number theory, given a prime number p, the p-adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; p-adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number p ...