SURREAL NUMBER Meaning and
Definition
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A surreal number is a mathematical concept that extends the real number system by introducing infinitesimals and infinite numbers. Coined by the mathematician John Horton Conway in 1974, surreal numbers are used to explore and analyze the behavior of infinitely large and infinitesimally small quantities.
In their most basic form, surreal numbers are constructed as a set of values. Each surreal number is a pair of two sets of previously constructed surreal numbers - one representing numbers smaller than itself, and the other representing numbers larger. These sets are called the left set and the right set, respectively.
Surreal numbers possess specific rules governing their comparison, addition, and multiplication. They are organized in a well-defined order, where each number is either smaller, equal to, or larger than another surreal number.
One of the key characteristics of surreal numbers is their ability to encompass infinite decimal expansions and fractions that cannot be represented by conventional real numbers. This property allows surreal numbers to bridge the gap between finite and infinite quantities, offering a powerful tool for solving complex mathematical problems involving infinite series, calculus, and analysis.
Surreal numbers have found applications in various areas of mathematics, including game theory, combinatorial game theory, and computer science. Their unique properties and the versatility they offer have made surreal numbers an essential concept in modern mathematics.
Etymology of SURREAL NUMBER
The word "surreal" was coined by the mathematician Donald Knuth in 1974 to describe a special class of numbers that he discovered. The term "surreal" was chosen because these numbers possess unique and unexpected properties, challenging the conventional notions of number systems.
The etymology of the word itself relates to the artistic movement called "surrealism", which emerged in the early 20th century. Surrealism sought to unlock the power of the unconscious mind and tap into the realm of dreams, fantasies, and irrational elements in order to create new artworks that defied logic and rationality. The mathematicians who came across Knuth's discoveries found parallels between the unexpected properties of the surreal numbers and the unconventional and unexpected nature of surrealist art, thus leading to the term "surreal number" being adopted to describe them.
