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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Differentials must be zeros, and the derivative dy/dx must be the quotient 0/0

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.The concept of an infinitesimal as a quantity less than any assignable magnitude yet unequal to zero is incoherent
      ?

      Think about whether this reason is strong or weak

    • 2.If infinitesimals are not valid non-zero quantities, then the increments in a ratio of evanescent quantities must themselves be zero
      ?

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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Berkeley's critique in 'The Analyst' concedes that calculus yields correct results, implying the 0/0 interpretation captures a genuine mathematical operation.
      ?

      Think about whether this reason is strong or weak

    • 2.Leibniz himself treated dy and dx as formal symbols subject to algebraic cancellation, making 0/0 a legitimate ratio under the law of continuity.
      ?

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    • 3.A ratio of two vanishing quantities preserves a determinate finite value as both approach zero simultaneously, making 0/0 well-defined in context.
      ?

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    Reason against 2 of 2
    ?
    • 1.Carnot's 'Réflexions sur la métaphysique du calcul infinitésimal' defends compensating errors, implying zeros in numerator and denominator systematically cancel.
      ?

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    • 2.If the derivative is understood as a limit of a process rather than a static quotient, then 0/0 names the indeterminate form whose resolution is the derivative's very definition.
      ?

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