Convergence on surreals

TL;DR

This paper introduces a new notion of convergence for surreal sequences based on their sign expansion, providing a potential framework for analyzing limits within surreal number theory.

Contribution

It proposes a novel convergence concept for surreal sequences utilizing sign expansion, advancing the understanding of limits in surreal number analysis.

Findings

Defines a convergence notion for surreal sequences

Uses sign expansion to characterize limits

Provides a foundation for further surreal analysis

Abstract

Using the sign expansion of the surreal numbers, we give a possible notion of convergence for surreal sequences.