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  • The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "

    From Alan Mackenzie@21:1/5 to wolfgang.mueckenheim@tha.de on Fri Mar 21 18:48:40 2025
    WM <wolfgang.mueckenheim@tha.de> wrote:
    On 21.03.2025 18:39, Jim Burns wrote:
    On 3/21/2025 3:50 AM, WM wrote:
    On 20.03.2025 23:25, Jim Burns wrote:

    For sets not.having a WM.size,
    Bob vanishing isn't a size.change.

    Only if reducing isn't reducing.

    What you (WM) think is reducing
    isn't reducing.

    You confuse the clear fact that in the reality of sets vanishing means reducing with the foolish claim that cardinality was a meaningful notion.

    Learn that even Cantor has accepted that the positive numbers have more reality than the even positive numbers.

    You mean something like positive numbers have a reality score of 5, and
    the even positive numbers only have a reality score of 3?

    He said that is not in conflict with the identical cardinality of both
    sets. And he was right!

    I doubt very much Cantor said such rubbish. He was a mathematician.

    "Coun[t]able" is simply another name for potential infinity.

    Not even close. Countable is an adjective defined in set theory,
    "potential infinity" is a fantasy noun, with no place in modern
    mathematics.

    Therefore vanishing odd numbers means reducing the reality of the set.

    By how much (on our scale of 1 to 10) does this reality get reduced?

    Therefore the sentence "What you (WM) think is reducing isn't
    reducing" exhibits you as a snooty dilettante who cannot distinguish
    between cardinality and reality.

    Hah! He's got to you, has he? Jim has spent some considerable effort
    in trying to get you (WM) to understand about infinite sets. It would
    appear you've failed to learn. You don't _want_ to learn. So I suppose
    we can expect you to initiate more nonsense threads about sets in the
    future. Not good.

    Regards, WM

    --
    Alan Mackenzie (Nuremberg, Germany).

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  • From WM@21:1/5 to joes on Mon Mar 24 20:29:25 2025
    On 24.03.2025 01:40, joes wrote:

    (Cardinality is maths.)

    Yes but a very primitive form of maths. Countably infinite sets can have
    may different properties. To forbid to investigate them is stupid orthodoxy.

    That's bullshit. Bijections are "complete".
    They should be complete. But complete bijecions are easily prove as
    such: They are injective for every surjection. Cantor's "bijections"
    fail to stand this test.
    Right, I forgot you don't believe in bijections. I don't understand
    what you mean by that test. Can you explain?

    When two sets have equal substance of definable elements then every
    injective mapping is surjective and every surjective mapping is injective.

    Regards, WM


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  • From joes@21:1/5 to All on Tue Mar 25 08:25:35 2025
    Am Mon, 24 Mar 2025 20:29:25 +0100 schrieb WM:
    On 24.03.2025 01:40, joes wrote:

    (Cardinality is maths.)
    Yes but a very primitive form of maths. Countably infinite sets can have
    may different properties. To forbid to investigate them is stupid
    orthodoxy.
    It is not forbidden. The superset relation explains everything.

    That's bullshit. Bijections are "complete".
    They should be complete. But complete bijecions are easily prove as
    such: They are injective for every surjection. Cantor's "bijections"
    fail to stand this test.
    Right, I forgot you don't believe in bijections. I don't understand
    what you mean by that test. Can you explain?
    When two sets have equal substance of definable elements then every
    injective mapping is surjective and every surjective mapping is
    injective.
    And you think Cantor bijected "dark numbers"?

    --
    Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
    It is not guaranteed that n+1 exists for every n.

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  • From WM@21:1/5 to joes on Tue Mar 25 20:17:58 2025
    On 25.03.2025 09:25, joes wrote:
    Am Mon, 24 Mar 2025 20:29:25 +0100 schrieb WM:

    When two sets have equal substance of definable elements then every
    injective mapping is surjective and every surjective mapping is
    injective.
    And you think Cantor bijected "dark numbers"?

    No, he did not know them. They cannot be bijected.

    Regards, WM

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