Surreal number is the largest number system where you use only the axiom of sets and one axiom of "less than" to construct numbers. Each number is constructed by putting together two sets, left and right, of which any number in the left set is less than those in the right set. Zero has empty sets for left and right. It contains real numbers, ordinals, and more. John H. Conway (of Game of Life fame) first discovered it when studying Go as a mathematical game. Donald Knuth (of TeX fame) gave it the name "surreal number" and wrote the first book about it in six days on a vacation with his wife.
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Surreal number is the largest number system where you use only the axiom of sets and one axiom of "less than" to construct numbers. Each number is constructed by putting together two sets, left and right, of which any number in the left set is less than those in the right set. Zero has empty sets for left and right. It contains real numbers, ordinals, and more. John H. Conway (of Game of Life fame) first discovered it when studying Go as a mathematical game. Donald Knuth (of TeX fame) gave it the name "surreal number" and wrote the first book about it in six days on a vacation with his wife.