The arithmetic of reversed positional games

✍ Scribed by Yõhei Yamasaki

• Book ID: 104326202
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 190 KB
• Volume: 174
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(96)00156-9

✦ Synopsis

Berlekamp et al. (1982)

and Conway (1976) showed that the real numbers can be regarded as the outcome of games. The purpose of this paper is to investigate the positional games introduced by Berge (1976), with the decision of winner reversed. We shall conclude that they are congruent to numbers modulo * provided no draw is possible, where * = (0 ( 0} denotes the non-numerical game with the earliest birthday (cf. [2,3]). We shall conclude also that a reversed positional game of second type is congruent to an integer modulo *.