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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sun, 20 Oct 2024 17:54:57 -0400
Organization: i2pn2 (i2pn.org)
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On 10/20/24 3:50 PM, WM wrote:
> On 20.10.2024 21:31, Richard Damon wrote:
>> On 10/20/24 10:26 AM, WM wrote:
>>> On 20.10.2024 13:56, Richard Damon wrote:
>>>> On 10/20/24 3:48 AM, WM wrote:
>>>
>>>>> All doubled numbers result in larger numbers. That cannot be avoided.
>>> ´
>>>> But since there isn't a "largest" number,
>>>
>>> There is completeness.
>>
>> Which meaning of "Completeness" do you mean?
> 
>> For set theory, the "Completeness" of the Natural Numbers says there 
>> is a suprema of the set
> 
> Completes means that all elements of a set are existing. The natural 
> numbers for instance are invariable. The subset of even numbers and the 
> subset of odd numbers are two halves having only half of the reality of 
> the natural numbers.
> 
> Regards, WM
> 
> 

Right, all exist, but in being infinite, that means that it doen't have 
an "end" and thus any logic that presumes an "end" isn't applicable.

Your problem is just that your idea of "completeness" assumes an implied 
finiteness, which the set doesn't have, thus, you logic can NEVER have a 
complete infinity, so your "actual infinity" just isn't actually 
infinite, but just wrong.

Your mind is just blowing up by the fact that half of an infinite set 
can be the same size as the whole, because Aleph_0 / 2 == Aleph_0