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    Classical non-standard analysis already permits neglectin... — Carmelics
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    Challenges→Inconsistent non-standard analysis has computational advantages over classical non-standard analysis in the theory of differentiation

    Classical non-standard analysis already permits neglecting higher-order infinitesimals via the standard part function without logical inconsistency.

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    Reasons For

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    • 1.The standard part function provides a rigorous mapping from hyperreals to reals, formally justifying infinitesimal neglect without contradiction.
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    • 2.Keisler's elementary calculus demonstrates that NSA computations yield identical results to classical analysis, validating the infinitesimal approach.
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    • 3.Higher-order infinitesimals (ε², ε³, etc.) are logically subordinate to first-order ones; their omission reflects a principled hierarchy, not inconsistency.
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    Reasons Against

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    • 1.The standard part function itself requires appeal to classical completeness axioms, making NSA dependent on classical logic rather than independent.
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    • 2.Neglecting higher-order infinitesimals via the standard part assumes a hidden ordering principle that lacks explicit justification within NSA's axioms.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Higher-order infinitesimals (ε², ε³, etc.) are logically subordinate to first-or...Inconsistent non-standard analysis has computational advantages over classical n...Keisler's elementary calculus demonstrates that NSA computations yield identical...Neglecting higher-order infinitesimals via the standard part assumes a hidden or...
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    The standard part function itself requires appeal to classical completeness axio...The standard part function provides a rigorous mapping from hyperreals to reals,...

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    2 (1 for, 1 against)
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