Surreal numbers
Números surreales
- Date
- c. 1970 · confidence low
- Place
- University of Cambridge, Cambridge, United Kingdom
- Credited to
- John Horton Conway
- Field
- Knowledge & symbols
What was discovered
Analysing Go endgames, Conway built a totally ordered proper class containing the real numbers together with infinite and infinitesimal numbers, defined recursively as pairs of sets of previously constructed numbers. Donald Knuth named and popularised the idea in his 1974 book 'Surreal Numbers'.
Wikidata gives no precise year; Conway developed the idea in the early 1970s at Cambridge while analysing Go endgames, publishing it himself in 'On Numbers and Games' (1976), after Knuth's earlier popularisation (1974).
What it led to
- Combinatorial game theory, formalised in 'On Numbers and Games' (1976)
- A unified new foundation for reals, ordinals and infinitesimals
Built on
- Dedekind cuts
- Hahn series