The continuum of the surreal numbers revisited.The surreal numbers defined through transfinite Cauchy fundamental sequences
Abstract
In this treatise on the theory of the continuum of the surreal numbers of J.H. Conway, is proved ,that the three different techniques and hierarchies of the continuums of the transfinite real numbers of Glayzal A. (1937) defined through transfinite power series , of the surreal numbers of J.H. Conway (1976) defined by Dedekind cuts ,and of the ordinal real numbers of K. E. Kyritsis (1992) defined by fundamental Cauchy transfinite sequences, give by inductive limit or union the same class and continuum of infinite numbers. This is quite remarkable and is the analogue in the transfinite numbers, of that the real numbers can be constructed either as decimal power series, or by Dedekind cuts, or by Cauchy fundamental sequences.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.05237
 Bibcode:
 2021arXiv211005237K
 Keywords:

 Mathematics  General Mathematics
 EPrint:
 This text of 64 pages is actually 5 consecutive papers published in the same proceedings of the same conference