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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
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Date: Mon, 22 Apr 2024 19:07:37 -0400
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On 4/22/24 11:35 AM, WM wrote:
> Le 21/04/2024 à 20:08, Jim Burns a écrit :
>> On 4/20/2024 12:23 PM, WM wrote:
>>> Le 19/04/2024 à 21:16, Jim Burns a écrit :
>>>> On 4/19/2024 11:05 AM, WM wrote:
>>
>>>>> 0, 1, 2, 3, ...,   w  = X
>>>>> |  |  |  |  |||    |
>>>>> 0, 2, 4, 6, ..., w*2  = Y
>>>
>>>> I answer and you refuse to see it because
>>>> ω isn't what you (WM) want ω to be.
>>>
>>> I assume that it is the first transfinite number,
>>> following directly upon all natural numbers.
>>
>> I answer and you refuse to see
>> what the first transfinite ordinal is.
> 
> The original set fits in (0, ω). The doubled set doesn't.
> 
> Regards, WM
> 

Of course it does, as every number < ω is finite, and any finte number 
doubled is also finite and thus < ω.

This is the strange nature of unbounded sets that breaks finite logic.