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Any element of a certain field equivalent to the real numbers augmented with infinite and infinitesimal numbers (respectively larger and smaller (in absolute value) than any positive real number).
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences
Examples
- Conway's construction of surreal numbers relies on the use of transfinite induction.
- Conway's approach was to build numbers from scratch using a construction inspired by his game theory research; the resulting class of surreal numbers proved much larger than the class of real numbers.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Coined by American computer scientist and mathematician Donald Knuth in his novelette Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness (1974). The concept had been developed by British mathematician John Conway for his game theoretic research of the board game go. Conway had simply called them numbers, but subsequently adopted Knuth's term and used it in his book On Numbers and Games (1976).
Across languages
Translations
3 source translations are retained for this English entry.
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French:
nombre surréel
— element of an extension of the real numbers that includes infinite numbers and infinitesimals
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Italian:
numero surreale
— element of an extension of the real numbers that includes infinite numbers and infinitesimals
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Portuguese:
número surreal
— element of an extension of the real numbers that includes infinite numbers and infinitesimals
