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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 The claim's scope is implicitly restricted to a proper subset of function pairs, making the theorem's generality philosophically overstated when presented without that qualification.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Standard mathematical practice includes explicitly stating hypotheses; qualified theorems aren't presented as universal unless proven universal.
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    • 2.The claim conflates informal presentation style with logical scope—restrictions in proofs are logically part of the theorem itself.
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    • 3.Many theorems genuinely apply broadly because their conditions are minimal; dismissing this as 'overstated' assumes too much about intent.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Mathematical theorems often apply only to well-behaved function classes (continuous, differentiable, measurable) but are stated universally.
      ?

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    • 2.Presenting restrictions only in proofs rather than theorem statements misleads readers about actual scope and applicability.
      ?

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    • 3.Philosophical claims about theorems' generality should match how they're formally presented to avoid overstating their reach.
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