"... in the author's opinion this is the most important advantage of nonstandard analysis over standard analysis: To have convenient (almost "explicit") representations of certain objects like Hahn-Banach limits for which by standard methods more or less only their mere existence can be proved with the axiom of choice."
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Martin Andreas Väth:
https://en.wikiquote.org/wiki/Nonstandard_analysis
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Nonstandard analysis
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