Common · Knowledge
Superreal number
Class of extensions of the real numbers
In abstract algebra, the superreal numbers are a class of extensions of the real numbers, introduced by H. Garth Dales and W. Hugh Woodin as a generalization of the hyperreal numbers and primarily of interest in non-standard analysis, model theory, and the study of Banach algebras. The field of superreals is itself a subfield of the surreal numbers.
From Wikipedia
In abstract algebra, the superreal numbers are a class of extensions of the real numbers, introduced by H. Garth Dales and W. Hugh Woodin as a generalization of the hyperreal numbers and primarily of interest in non-standard analysis, model theory, and the study of Banach algebras. The field of superreals is itself a subfield of the surreal numbers. Dales and Woodin's superreals are distinct from the super-real numbers of David O. Tall, which are lexicographically ordered fractions of formal power series over the reals.
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Hyperreal number
Element of a nonstandard model of the reals, which can be infinite or infinitesimal
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Surreal number
A totally ordered proper class containing the real numbers as well as hyperreal numbers such as infinity and infinitesimals.
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Subfactorial
Mathematics
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Ideal number
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Essential supremum
Notions of infimum and supremum
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Abstract algebra
Branch of mathematics studying algebraic structures and their relations