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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 TIME(n^k) is always a proper subset of TIME(n^{k+1}) for all natural numbers k

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The proof that n^k*log(n^k)/n^{k+1} approaches 0 establishes a limit condition, but the theorem yields only the existence of some language separating the classes, not a constructive or uniform witness.
      ?

      Think about whether this reason is strong or weak

    • 2.Quine's criterion for ontological commitment requires that existential claims in formal systems carry genuine ontological weight only when the existents are specifiable, not merely provably existent.
      ?

      Think about whether this reason is strong or weak

    • 3.A proper subset relation grounded solely in non-constructive existence proofs may be ontologically deficient in ways that undermine the modal force of 'always' in the original claim.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The Time Hierarchy Theorem presupposes a specific multi-tape Turing machine model, and proper inclusion results may not transfer across all computationally equivalent models.
      ?

      Think about whether this reason is strong or weak

    • 2.Model-relative results in complexity theory function as framework-dependent truths, not absolute set-theoretic facts about TIME classes as abstractly defined.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The Deterministic Time Hierarchy Theorem holds when the limit of t1(n)log(t1(n))/t2(n) equals 0
      ?

      Think about whether this reason is strong or weak

    • 2.The functions n^k and n^{k+1} satisfy this limit condition
      ?

      Think about whether this reason is strong or weak

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