Analysis {nonstandard analysis} can use infinitesimals that can never get large. In nonstandard analysis, numbers, metrics, and spaces always have nearby values.
contradiction
Non-standard analysis can introduce contradictions, because added infinitesimals do not necessarily stay small. Infinitesimals can violate Archimedes principle {non-Archimedian}.
theorem
For proposition sets, if finite proposition subsets are true in standard analysis, whole proposition set is true in nonstandard analysis {compactness theorem}.
Mathematical Sciences>Calculus>Analysis>Kinds
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0224