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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: how
Date: Fri, 19 Apr 2024 19:38:49 -0400
Organization: i2pn2 (i2pn.org)
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On 4/19/24 11:39 AM, WM wrote:
> Le 19/04/2024 à 00:40, Richard Damon a écrit :
>> On 4/18/24 11:08 AM, WM wrote:
>>> Le 18/04/2024 à 01:27, Phil Carmody a écrit :
>>>> Richard Damon <richard@damon-family.org> writes:
>>>
>>>>> That means that YOUR logic system is proven INCONSISTENT, and thus
>>>>> BLOWN UP.
>>>>
>>>> And that is where the intrigue lies.
>>>
>>> My logic system says: ω is amidst the interval (0, ω2) because in the 
>>> image of the function f(x) = x*2 there are as many ordinals in (ω, 
>>> ω2) as in (0, ω).
>>>
>>
>> And if your logic doesn't understand that the "ordinals" in (ω, ω*2) 
>> are different than those of (1, 2, 3, ...) it is just broken.
> 
> Of course they are different since all those of (1, 2, 3, ...) have been 
> doubled and therefore cannot remain the same set.

Nope, sjnce every natural number has aleph_0 natural numbers after it, 
they are never "used up", but there are always more.

Your logic just breaks on unbounded sets.

>>
>> Any finite number *2 will be less than ω.
> 
> Not if all those which could emerge from doubling are doubled too.

Yep, since you can't "use up" an infinte set that way.

> 
> Regards, WM