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    A proper subset relation grounded solely in non-construct... — Carmelics
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    Challenges→TIME(n^k) is always a proper subset of TIME(n^{k+1}) for all natural numbers k

    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.

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    Key Terms

    Always (in modal context)(as used in logic)
    In this context, it means something must be true in every possible situation or case.
    Ontologically deficient(as used in metaphysics)
    Missing or lacking something important about what actually exists or what counts as real.
    Ontology/Ontological(in metaphysics)
    The philosophical study of what actually exists or is real, as opposed to what merely seems to exist or what we can know about things.
    Subset relation(in formal logic)
    A mathematical relationship where one group is entirely contained within another—like how all squares are rectangles, but not all rectangles are squares.
    modal(in logic and metaphysics)

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    Dealing with possibility and necessity—questions about what could be true, what must be true, and what's merely contingent (could go either way).
    modal force(as used in modal logic)
    The power or strength of a statement about necessity, possibility, or contingency—what makes something 'must be' versus 'might be'.
    non-constructive existence proof(in mathematical logic)
    A proof that proves something exists without actually showing you how to find or build it—like proving a solution exists without explaining how to find it.

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    Proof of definition segments1 linkedModality & Possibility1 linked

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

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