Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

After serious thinking Richard Damon wrote :

On 10/20/24 3:40 AM, WM wrote:

On 20.10.2024 00:08, Jim Burns wrote:

On 10/19/2024 2:28 PM, WM wrote:

 

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The contradiction is independent of infinity.
It is your claim that

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infinitely.many exchanges in an infinite set
(vanishing Bob)

 Every exchange is _one_ lossless exchange.

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exchanging two objects
can result in the loss of one of them.

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I fixed that for you.

 It is nonsense like:
∀n ∈ ℕ: |{2, 4, 6, ..., 2n}|/|{1, 2, 3, 4, 5, 6, ..., 2n} = 1/2
but |{2, 4, 6, ...}|/|{1, 2, 3, 4, 5, 6, ...} = 1.
 Regards, WM
 

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Right, but
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|{2, 4, 6, ...}| is Aleph_0, as is |{1, 2, 3, 4, 5, 6, ...}|
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Which is a value you have admitted your mathematics doesn't have.
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You have admitted that your "actual infinity" isn't actually infinite, and just a term used to lie.
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I(nfinity isn't just "really big numbers" like you want to treat it, but a set of numbers with DIFFERENT properties from the finite.

That's it. If a proper subset results in a different cardinality, it is a finite set. If a set is not finite, it is infinite. What he doesn't like is the bijective mapping between infinitely many elements without seeing their set membership cards first. :)