Word.ws English Dictionary

surreal number

surreal number noun: 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).

Noun

surreal number (plural surreal numbers)

  1. 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).
    • 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.

Forms of surreal number

pluralsurreal numbers

Origin of surreal number

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).

Questions about surreal number

What does surreal number mean?
Surreal number means 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).
What part of speech is surreal number?
Surreal number is a noun.
What is the plural of surreal number?
The plural of surreal number is surreal numbers.

Words near surreal number in the dictionary

  1. surreach
  2. surreached
  3. surreaches
  4. surreaching
  5. surreal
  6. surreal number
  7. surreal numbers
  8. surrealia
  9. surrealish
  10. surrealism
  11. surrealisms

Source and license

Adapted from Wiktionary: surreal number (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Cite this entry: “surreal number.” Word.ws, https://word.ws/surreal_number. Based on Wiktionary, CC BY-SA 4.0.