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ELEMENTARY PRACTICE OF NONSTANDARD ANALYSIS Lesson 0 quite classic Infinitesimals
with a slight non standard flavour Limits
entirely non standard Continuity
46 other sections not shown
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assume asymptotic behaviour axiom of choice basis binary relation boundary layer classical Comments compact computation conservative extension dard defined deformation differential Edited equation equivalent exists external formula external sets f is continuous filter finitary finite element formal free variables function geometric halo Hausdorff Hausdorff space hence ideal element implies infinitely large infinitesimal instance integral curve INTERNAL SET THEORY intuitive isomorphism lemma lesson Lie algebra limit point linear mapping f mathematics metric space natural integers neighbourhood Non-Standard Analysis open sets parameter permanence principle polynomial problem Proof of theorem proposition prove recall resp S-continuous S-convergent satisfy shadow singular perturbation solution stan standard elements standard mapping standard open standard point standard sequence standard set standard subset statement theorem in Z.F. theory thickeness order tion topological space topology totally ordered transfer property ultrafilter unique values vector field