Encyclopedia > On Numbers and Games

  Article Content

On Numbers and Games

On Numbers and Games is a mathematics book by John Conway, published by Academic Press Inc in 1976, ISBN 0121863506.

It uses sets to define a universe of numbers (whole numbers, fractional numbers and some very strange surreal numbers of no use to the general public) and as a by-product, uses the same method to define some "games".

At the start the only set you have is the empty set (ie the set with no members). The number 0 is defined as the result of comparing the empty set with the empty set (written as {|} ). Now you can compare the set comprising 0 with the empty set, {0|}, which is results in the number 1; you can compare the empty set with 0, {|0}, which is results in -1; and you can compare 0 with 0, {0|0}, which is the first "game" and is called * (star).

Star is not a "game" as such but is the value for a common position in many games. In a game played between Left and Right, if the position has the value 1 (a number) then it is a win for Right. If -1 a win for Left, if 0 a win for the second person to play; and if * a win for the first player.

The book is in two, (0,1|}, parts. The zeroth part is about numbers, the first part about games - both the values of games and also some real games that can be played such as Nim, Hackenbush[?], Col[?] and Snort[?] amongst the many described.

For a more detailed treatment of the mathematics involved, see surreal numbers.

See also: Winning Ways for your Mathematical Plays.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article

... - 3rd century - 4th century Decades: 190s 200s 210s 220s 230s - 240s - 250s 260s 270s 280s 290s Years: 237 238 239 240 241 - 242 - 243 244 245 246 ...

This page was created in 24 ms