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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that Lawless sequences, lacking any rule of extension, cannot be the subject of proofs or calculations in the way rule-governed irrationals can.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Non-constructive objects (e.g., Dedekind cuts, real numbers via completeness axiom) are subject to rigorous proofs despite lacking explicit rules.
      ?

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    • 2.A sequence's unprovability about one property doesn't prevent all proofs about it; lawless sequences have provable features (e.g., boundedness assumptions).
      ?

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    • 3.The distinction between 'rule-governed' and 'lawless' conflates computability with mathematical legitimacy; both can be axiomatically characterized.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Proofs require recursive procedures or algorithms; lawless sequences have no computable rule, so formal derivation becomes impossible.
      ?

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    • 2.Algebraic irrationals (like √2) satisfy polynomial equations enabling systematic calculation; lawless sequences lack any defining property.
      ?

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    • 3.Mathematical discourse presupposes shared, reproducible methods; lawless sequences resist intersubjective verification or communication.
      ?

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