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\title{Constructing the Reals as Dedekind Cuts of Rationals}
\author{Jacques D. Fleuriot and Lawrence C. Paulson}
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\begin{abstract}
The type of real numbers is constructed from the positive rationals using the method of Dedekind cuts. This development, briefly described in papers by the authors \cite{fleuriot-real-analysis,fleuriot-jcm}, follows the textbook presentation by Gleason~\cite{gleason-fundamentals}.
It's notable that the first formalisation of a significant piece of mathematics, by Jutting~\cite{jutting77} in 1977, involved a similar construction.
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\paragraph*{Remark.}
This development was part of the Isabelle distribution from about 1999 to 2022. 
It has been transferred to the AFP, where it may be more useful.

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