Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

On 12/23/24 3:52 AM, WM wrote:

On 23.12.2024 01:05, FromTheRafters wrote:

WM brought next idea :
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The function E(n) decreases from infinity to zero because in set theory ℕ \ {1, 2, 3, ...} =  { } is an accepted formula.

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In what way is it decreasing?

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One by one. Every endsegment transforms a natural number from content inside to index outside. That is guaranteed by mathematics:
∀k ∈ ℕ : ∩{E(0), E(1), E(2), ..., E(k+1)} = ∩{E(0), E(1), E(2), ..., E(k)} \ {k+1}. Note the universal quantifier.
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Regards, WM
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 Except that you don't understand that infinitiy minus 1 is still infinity, and thus did not "decrease".

 All you have shown is that your logic is built of FALSE ASSUMPTIONS because it uses rules that only hold for FINITE quantities, because you thing everything is just like the finite, and thus your logic blows up and lies when it needs to handle the infinite.