Abstract
The transreal numbers, proposed by James Anderson, are an extension of the real numbers. This new set is closed under the four arithmetical operations: addition, subtraction, multiplication and division. In particular, division by zero is allowed. Anderson introduced the transreals intuitively and axiomatically. In this paper we propose a construction of the transreals from the reals. Thus the transreal numbers and their arithmetic arise as consequences of real numbers. We dene the set of transreal numbers as a certain class of subsets of ordered pairs of real numbers and we show that, in an appropriate sense, there is a copy of the real numbers in this new set.
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