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    If a consistent alternative infinitesimal framework assig... — Carmelics
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    Challenges→If curves are infinilateral polygons, then the lengths of the sides of those polygons must be nilsquare infinitesimals.

    If a consistent alternative infinitesimal framework assigns nonzero squares to infinitesimals, then nilsquareness is not a necessary condition for infinilateral polygon sides.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Nonstandard analysis proves consistent frameworks exist where infinitesimals have nonzero squares without logical contradiction.
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    • 2.Nilsquareness was posited for smooth infinitesimal analysis, not derived from infinitesimal geometry's fundamental axioms.
      ?

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    • 3.If infinitesimal polygon sides exist in multiple consistent frameworks with different algebraic properties, their geometric role cannot depend on one property alone.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Nilsquareness is essential to infinitesimal calculus; removing it reconstructs classical analysis and eliminates infinitesimals' distinctive utility.
      ?

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    • 2.The claim conflates 'consistent frameworks exist' with 'nilsquareness is unnecessary'—consistency doesn't entail relevance to actual infinitesimal polygon geometry.
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    • 3.If infinitesimal sides have nonzero squares, they generate measurable area contributions, collapsing the infinitesimal distinction that polygon theory requires.
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    Related

    If curves are infinilateral polygons, then the lengths of the sides of those pol...If infinitesimal polygon sides exist in multiple consistent frameworks with diff...If infinitesimal sides have nonzero squares, they generate measurable area contr...Nilsquareness is essential to infinitesimal calculus; removing it reconstructs c...
    +3 moreShow less
    Nilsquareness was posited for smooth infinitesimal analysis, not derived from in...Nonstandard analysis proves consistent frameworks exist where infinitesimals hav...The claim conflates 'consistent frameworks exist' with 'nilsquareness is unneces...

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    claim
    Perspectives
    2 (1 for, 1 against)
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