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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)
Date: Sun, 20 Oct 2024 10:17:12 -0400
Organization: Peripheral Visions
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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:
>> 
>>>>
>>>> The contradiction is independent of infinity.
>>>> It is your claim that
>>>
>>> infinitely.many exchanges in an infinite set
>>> (vanishing Bob)
>> 
>> Every exchange is _one_ lossless exchange.
>>>
>>>> exchanging two objects
>>>> can result in the loss of one of them.
>>>
>>> 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
>> 
>
> Right, but
>
> |{2, 4, 6, ...}| is Aleph_0, as is |{1, 2, 3, 4, 5, 6, ...}|
>
> Which is a value you have admitted your mathematics doesn't have.
>
> You have admitted that your "actual infinity" isn't actually infinite, and 
> just a term used to lie.
>
> 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. :)