Abstract
AbstractAny set x is uniquely specified by the graph of the membership relation on the set obtained by adjoining x to the transitive closure of x. Thus any operation on sets can be looked at as an operation on these graphs. We look at the operations of ordinal arithmetic of sets in this light. This turns out to be simplest for a modified ordinal arithmetic based on the Zermelo ordinals, instead of the usual von Neumann ordinals. In this arithmetic, addition of sets corresponds to concatenating graphs, and multiplication corresponds to replacing each edge of a graph by a copy of another graph. Characterizations for the von Neumann case are also given.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
