Nonstandard Analysis

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3 domain-specific abstractions whose origin domain is Nonstandard Analysis.

• Hyperreal number — An element of a proper ordered-field extension of the real numbers containing infinitesimal and infinite elements and satisfying a transfer principle.
• Microcontinuity — The nonstandard-analysis form of continuity requiring infinitely close inputs to have infinitely close outputs.
• Monad (nonstandard analysis) — The set of hyperreal points infinitesimally close to a given hyperreal point, with a finite point's monad containing exactly one real standard part.