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    If 'absolutely infinite' means having no cardinal number,... — Carmelics
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    Challenges→The totality of transfinite cardinal numbers is absolutely infinite in a sui generis non-arithmetical sense, rather than having a cardinal number of its own.

    If 'absolutely infinite' means having no cardinal number, this is precisely what ZFC already says about proper classes, making the 'sui generis' qualifier redundant rather than explanatory.

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    Key Terms

    Proper classes(as used in set theory)
    In set theory, collections of things that are too large or too weird to be treated as ordinary 'sets' (think of them as super-big collections).
    ZFC(Classical set theory as a foundation for mathematics)
    The axiom system ZF plus the axiom of choice (AC).
    cardinal number(There are infinitely many cardinals but no set that collects them all.)
    A number used to measure the size (cardinality) of sets.
    redundant(contrasting with what the formula should actually be)
    Unnecessary or repetitive—extra without serving a purpose, like having two copies of the same tool.
    sui generis(Used to characterize goodness if naturalistic definitions all fail.)

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    A notion that can only be understood in its own terms — in this context, goodness can only be understood in evaluative, not empirical or naturalistic, terms.

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    The totality of transfinite cardinal numbers is absolutely infinite in a sui gen...

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