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  2. Real number - Wikipedia

    en.wikipedia.org/wiki/Real_number

    In mathematics real is used as an adjective, meaning that the underlying field is the field of the real numbers (or the real field). For example, real matrix, real polynomial and real Lie algebra. The word is also used as a noun, meaning a real number (as in "the set of all reals").

  3. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    Computable number: A real number whose digits can be computed by some algorithm. Period: A number which can be computed as the integral of some algebraic function over an algebraic domain. Definable number: A real number that can be defined uniquely using a first-order formula with one free variable in the language of set theory.

  4. Category:Real numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Real_numbers

    In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. The term "real number" is a retronym coined in response to "imaginary number". Together with the p-adic numbers, the reals are a limit set of the rational numbers. Real numbers may be ...

  5. Real algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Real_algebraic_geometry

    Real algebra is the part of algebra which is relevant to real algebraic (and semialgebraic) geometry. It is mostly concerned with the study of ordered fields and ordered rings (in particular real closed fields ) and their applications to the study of positive polynomials and sums-of-squares of polynomials .

  6. 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 ...

  7. Algebraic number - Wikipedia

    en.wikipedia.org/wiki/Algebraic_number

    As another example, the complex number + is algebraic because it is a root of x 4 + 4. All integers and rational numbers are algebraic, as are all roots of integers. Real and complex numbers that are not algebraic, such as π and e, are called transcendental numbers.

  8. Distributive property - Wikipedia

    en.wikipedia.org/wiki/Distributive_property

    Examples of structures with two operations that are each distributive over the other are Boolean algebras such as the algebra of sets or the switching algebra. Multiplying sums can be put into words as follows: When a sum is multiplied by a sum, multiply each summand of a sum with each summand of the other sum (keeping track of signs) then add ...

  9. Positive real numbers - Wikipedia

    en.wikipedia.org/wiki/Positive_real_numbers

    Including 0, the set has a semiring structure (0 being the additive identity), known as the probability semiring; taking logarithms (with a choice of base giving a logarithmic unit) gives an isomorphism with the log semiring (with 0 corresponding to ), and its units (the finite numbers, excluding ) correspond to the positive real numbers.

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