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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Thu, 30 Jan 2025 16:59:22 -0500
Organization: Peripheral Visions
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WM explained on 1/30/2025 :
> On 30.01.2025 20:54, FromTheRafters wrote:
>> WM explained on 1/30/2025 :
>>> On 30.01.2025 11:41, FromTheRafters wrote:
>>>> WM formulated the question :
>>>>> On 29.01.2025 15:04, FromTheRafters wrote:
>>>>>> WM explained on 1/29/2025 :
>>>>>>> On 29.01.2025 10:38, FromTheRafters wrote:
>>>>>>>
>>>>>>>> Omega has no immediate predecessor.
>>>>>>>
>>>>>>> What is immediately before ω?
>>>>>>
>>>>>> Nothing, it is the initial member of the transfinite ordinals. just as 
>>>>>> zero is the initial member of the finite ordinals.
>>>>>
>>>>> There is something before zero.
>>>>
>>>> Not in the ordinals, which is what you say the context is this time.
>>>
>>> Not in the known ordinals. But if anything else, then name it, and how 
>>> many of these are there.
>>>>
>>>>>>> And how long is the distance from ω to a natnumber?
>>>>>>
>>>>>> This makes no sense.
>>>>>
>>>>> It is research.
>>>>
>>>> Is there a 'distance' metric in the ordinals?
>>>>
>>>> ============================================
>>>> AI Overview
>>>>
>>>> No, there is no inherent "distance" metric in ordinal numbers
>>>
>>> Wrong. The ordinals 7 and 27 have the distance 27 - 7 = 20.
>> 
>> Finite ordinals are like finite cardinalities.
>
> Fine. Why do you mention this triviality?

Because you treat ordinals as if they were cardinals.