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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.