Conway’s games
E637294
Conway’s games are a class of combinatorial games introduced by mathematician John Horton Conway, forming the foundation of surreal numbers and studied for their rich algebraic and strategic properties.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Conway’s games canonical | 1 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
class of combinatorial games
ⓘ
mathematical structure ⓘ |
| component |
Left options set
ⓘ
Right options set ⓘ |
| documentedIn |
On Numbers and Games
NERFINISHED
ⓘ
Winning Ways for your Mathematical Plays NERFINISHED ⓘ |
| field |
combinatorial game theory
ⓘ
mathematics ⓘ |
| formalDefinition | games defined recursively by sets of left and right options ⓘ |
| foundationOf | surreal numbers ⓘ |
| hasConcept |
cold games
ⓘ
fuzzy games ⓘ hot games ⓘ infinitesimal games ⓘ loopy games (in extended theory) ⓘ numbers as games ⓘ short games (finite birthday) ⓘ |
| hasInfluenceOn |
mathematical foundations of game values
ⓘ
modern combinatorial game theory ⓘ research on surreal numbers ⓘ |
| hasProperty |
finite positions in basic theory
ⓘ
forms a field when restricted to numbers ⓘ no chance moves ⓘ ordered abelian group structure under addition ⓘ partizan games framework ⓘ perfect information ⓘ rich algebraic structure ⓘ supports addition ⓘ supports comparison ⓘ supports multiplication (via surreal numbers) ⓘ supports negation ⓘ well-founded game trees in basic theory ⓘ |
| hasRule |
Left chooses from left options
ⓘ
Right chooses from right options ⓘ a game is an ordered pair of sets of games (L,R) ⓘ player unable to move loses (normal play convention) ⓘ players move alternately ⓘ |
| introducedBy | John Horton Conway NERFINISHED ⓘ |
| relatedTo | surreal numbers ⓘ |
| studiedFor |
algebraic properties
ⓘ
applications in game analysis ⓘ strategic properties ⓘ |
| supportsOperation |
comparison via outcome classes
ⓘ
disjunctive sum of games ⓘ negation of games by swapping roles of players ⓘ |
| timeOfIntroduction | early 1970s ⓘ |
| usedIn |
analysis of impartial and partizan games
ⓘ
formalization of game values ⓘ theory of surreal numbers ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.