surreal number
Word Rarity
Rare
Frequency: Zipf frequency 3.59 in modern English
17
Scrabble Score
13
Letters
4
Syllables
9
Unique Chars
Meaning
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).
Example Sentences
- "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."
- "• A surreal number X=(X_L,X_R) consists of two sets X_L and X_R of surreal numbers, such that no element from X_L is greater than any element from X_R. • A surreal number Y=(Y_L,Y_R) is greater than another surreal number X=(X_L,X_R), X
- "Here we shall follow Conway's exposition rather closely. Let L and R be two sets of numbers. Assume that no member of L is greater than or equal to any member of R. Then #92;#123;L#92;vertR#92;#125; is a surreal number. All surreal numbers are constructed in this fashion."
Etymology
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).