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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 Mathematical practice across analysis, geometry, and number theory proceeded rigorously for centuries without set-theoretic foundations.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Historical mathematicians used implicit set-theoretic concepts (collections, domains, quantification) without formalizing them.
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    • 2.Rigor is relative to era; pre-Cauchy 'rigor' tolerated infinitesimals and divergent series now recognized as inadequately justified.
      ?

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    • 3.Set theory revealed hidden paradoxes in informal practice (like unrestricted comprehension), showing earlier foundations were incomplete.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Euler, Gauss, and Cauchy produced theorems still considered valid today without referencing set theory or its axioms.
      ?

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    • 2.Rigorous mathematical practice requires clear definitions and logical proof structure, which existed centuries before Cantor.
      ?

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    • 3.Set-theoretic foundations were developed to formalize existing mathematics, not to enable it; the practice preceded the framework.
      ?

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