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  2. Rational number - Wikipedia

    en.wikipedia.org/wiki/Rational_number

    In mathematics, "rational" is often used as a noun abbreviating "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 ...

  3. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.

  4. Number - Wikipedia

    en.wikipedia.org/wiki/Number

    A rational number is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator. Negative denominators are allowed, but are commonly avoided, as every rational number is equal to a fraction with positive denominator.

  5. Algebraic number - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number

    All rational numbers are algebraic. Any rational number, expressed as the quotient of an integer a and a (non-zero) natural number b, satisfies the above definition, because x = ⁠ a / b ⁠ is the root of a non-zero polynomial, namely bx − a.

  6. Real number - Wikipedia

    en.wikipedia.org/wiki/Real_number

    Firstly both definitions suppose that rational numbers and thus natural numbers are rigorously defined; this was done a few years later with Peano axioms. Secondly, both definitions involve infinite sets (Dedekind cuts and sets of the elements of a Cauchy sequence), and Cantor's set theory was published several years later.

  7. Construction of the real numbers - Wikipedia

    en.wikipedia.org/wiki/Construction_of_the_real...

    An axiomatic definition of the real numbers consists of defining them as the elements of a complete ordered field. [2] [3] [4] This means the following: The real numbers form a set, commonly denoted , containing two distinguished elements denoted 0 and 1, and on which are defined two binary operations and one binary relation; the operations are called addition and multiplication of real ...

  8. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    In mathematics a rational number is a number that can be represented by a fraction of the form ⁠ a / b ⁠, where a and b are integers and b is not zero; the set of all rational numbers is commonly represented by the symbol Q or ⁠ ⁠, which stands for quotient.

  9. Definable real number - Wikipedia

    en.wikipedia.org/wiki/Definable_real_number

    A real number is a constructible number if there is a method to construct a line segment of length using a compass and straightedge, beginning with a fixed line segment of length 1. Each positive integer, and each positive rational number, is constructible. The positive square root of 2 is constructible.