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  1. Real number From Simple English Wikipedia, the free encyclopedia A real number is a rational or irrational number, and is a number which can be expressed using decimal expansion. Usually when people say "number", they usually mean "real number". The official symbol for real numbers is a bold R, or a blackboard bold
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    What is a real number?
    In mathematics, a real number or real is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion ).
    en.wikipedia.org/wiki/Real_number
    What is the symbol for the set of real numbers?
    The set of real numbers is denoted using the symbol R or . Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced.
    en.wikipedia.org/wiki/Real_number
    When was the first set of real numbers defined?
    The first rigorous definition was published by Georg Cantor in 1871. In 1874, he showed that the set of all real numbers is uncountably infinite but the set of all algebraic numbers is countably infinite. Contrary to widely held beliefs, his first method was not his famous diagonal argument, which he published in 1891.
    en.wikipedia.org/wiki/Real_number
    Is the set of all real numbers uncountable?
    The set of all real numbers is uncountable; that is: while both the set of all natural numbers and the set of all real numbers are infinite sets, there can be no one-to-one function from the real numbers to the natural numbers: the cardinality of the set of all real numbers (denoted c {displaystyle {mathfrak {c}}} and called cardinality of the ...
    en.wikipedia.org/wiki/Real_number
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    Real number - Wikipedia

    https://en.wikipedia.org/wiki/Real_number

    In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion). The adjective real in this context was introduced in the 17th century by René Descartes, who distinguished

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    Simple fractions were used by the Egyptians around 1000 BC; the Vedic "Shulba Sutras" ("The rules of chords") in c. 600 BC include what may be the first "use" of irrational numbers. The concept of irrationality was implicitly

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    The real number system can be defined axiomatically up to an isomorphism, which is described hereafter. There are also many ways to construct "the" real number system, and a popular

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    Basic properties
    • Any non-zero real number is either negative or positive.
    • The sum and the product of two non-negative real numbers is again a non-negative real number, i.e., they are closed under these operations, and form a positive cone,

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    Real numbers and logic
    The real numbers are most often formalized using the Zermelo–Fraenkelaxiomatization of set theory, but some mathematicians study the

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    The real numbers can be generalized and extended in several different directions:
    • The complex numbers contain solutions to all polynomial

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    Mathematicians use the symbol R, or, alternatively, , the letter "R" in blackboard bold (encoded in Unicode as U+211D ℝ DOUBLE-STRUCK CAPITAL R (HTML ℝ · ℝ, ℝ)), to represent the setof all real numbers. As this set is naturally

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  4. Real number - Simple English Wikipedia, the free encyclopedia

    https://simple.wikipedia.org/wiki/Real_number

    Jump to navigation Jump to search. A real number is a rational or irrational number, and is a number which can be expressed using decimal expansion. Usually when people say "number", they usually mean "real number". The official symbol for real numbers is a bold R, or a blackboard bold. R {\displaystyle \mathbb {R} }

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    • Construction of the real numbers - Wikipedia

      https://en.wikipedia.org/wiki/Construction_of_the_real_numbers

      In mathematics, there are several equivalent ways of defining the real numbers. One of them is that they form a complete ordered field that does not contain any smaller complete ordered field. Such a definition does not prove that such a complete ordered field exists, and the existence proof consists to construct a mathematical structure that satisfies the definition.
      The article presents several such constructions. They are equivalent in the sense that, given the …

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    • Số phức – Wikipedia tiếng Việt

      https://vi.wikipedia.org/wiki/Số_phức
      • Nhà toán học người Ý R. Bombelli (1526-1573) đã đưa định nghĩa đầu tiên về số phức, lúc đó được gọi là số "không thể có" hoặc "số ảo" trong công trình Đại số (Bologne, 1572) công bố ít lâu trước khi ông mất. Ông đã định nghĩa các số đó (số phức) khi nghiên cứu các phương trình bậc ba và đã đưa ra căn bậc hai của − 1 {\displaystyle -1} . Nhà toán học người Pháp D’Alembert và…
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