Two concrete new constructions of the real numbers

@article{Knopfmacher1988TwoCN,
  title={Two concrete new constructions of the real numbers},
  author={Arnold Knopfmacher and John Knopfmacher},
  journal={Rocky Mountain Journal of Mathematics},
  year={1988},
  volume={18},
  pages={813-824}
}
Two new methods are put forward for constructing the complete ordered field of real numbers out of the ordered field of rational numbers. The methods are motivated by some known theorems on so-called Engel and Sylvester series. Amongst advantages of the methods are the facts that they do not require an arbitrary choice of "base", or any equivalence classes or similar constructs. Introduction. By old theorems of Lambert (1770) and Engel (1913) (see Perron [2]), every real number A has a unique… 

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