: Mathématiques: construction of the real numbers

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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 of constructing a mathematical structure that satisfies the definition.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Construction_of_the_real_numbers)

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