Non-standard analysis provides simpler and more intuitive... — Carmelics

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Non-standard analysis provides simpler and more intuitive proofs of many theorems of standard real analysis.

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Reasons For

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Reason for

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1.The approaches pioneered by Robinson and Nelson yield proofs of theorems in standard real analysis.
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2.These proofs are, in some sense, simpler than those produced by standard real analysis methods.
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Reasons Against

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Reason against 1 of 2

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1.Non-standard analysis requires accepting a stronger metatheory (ZFC + ultrafilter lemma or IST) than standard analysis demands.
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2.A proof system that presupposes more powerful foundational machinery cannot be deemed simpler in any epistemically rigorous sense.
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3.Intuitive accessibility at the level of object-language reasoning is offset by increased opacity at the foundational level, yielding no net simplicity gain.
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Reason against 2 of 2

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