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  2. Real number - Wikipedia

    en.wikipedia.org/wiki/Real_number

    The long real line pastes together ℵ 1 * + ℵ 1 copies of the real line plus a single point (here ℵ 1 * denotes the reversed ordering of ℵ 1) to create an ordered set that is "locally" identical to the real numbers, but somehow longer; for instance, there is an order-preserving embedding of ℵ 1 in the long real line but not in the real ...

  3. Class number problem - Wikipedia

    en.wikipedia.org/wiki/Class_number_problem

    Class number problem. In mathematics, the Gauss class number problem ( for imaginary quadratic fields ), as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields (for negative integers d) having class number n. It is named after Carl Friedrich Gauss.

  4. 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 ...

  5. Extended real number line - Wikipedia

    en.wikipedia.org/wiki/Extended_real_number_line

    Contents. Extended real number line. This article is about the extension of the reals with +∞ and −∞. For the extension by a single point at infinity, see Projectively extended real line. In mathematics, the extended real number system a is obtained from the real number system by adding two infinity elements: and b where the infinities ...

  6. Definable real number - Wikipedia

    en.wikipedia.org/wiki/Definable_real_number

    Informally, a definable real number is a real number that can be uniquely specified by its description. The description may be expressed as a construction or as a formula of a formal language. For example, the positive square root of 2, , can be defined as the unique positive solution to the equation , and it can be constructed with a compass ...

  7. Real analysis - Wikipedia

    en.wikipedia.org/wiki/Real_analysis

    Real analysis is an area of analysis that studies concepts such as sequences and their limits, continuity, differentiation, integration and sequences of functions. By definition, real analysis focuses on the real numbers, often including positive and negative infinity to form the extended real line.

  8. Computable number - Wikipedia

    en.wikipedia.org/wiki/Computable_number

    In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm. They are also known as the recursive numbers, [ 1] effective numbers[ 2] or the computable reals[ 3] or recursive reals. [ 4] The concept of a computable real number was introduced by Émile Borel in ...

  9. Number - Wikipedia

    en.wikipedia.org/wiki/Number

    Every real number corresponds to a point on the number line. The following paragraph will focus primarily on positive real numbers. The treatment of negative real numbers is according to the general rules of arithmetic and their denotation is simply prefixing the corresponding positive numeral by a minus sign, e.g. −123.456.