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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.math
Subject: Re: The set of necessary FISONs
Date: Tue, 4 Mar 2025 10:07:43 +0100
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On 04.03.2025 02:05, Richard Damon wrote:
> On 3/3/25 4:10 AM, WM wrote:

> They are just an artifact that your logic blew up when N_def became 
> infinite, blinding you to the truth.

By induction the number of numbers can never become an actually infinite 
quantity, larger than all finite numbers.
> 
>>>
>>> What is the highest expressable number?
>>
>> That does not exist because with n also n+1 is expressable.
> 
> So, why isn't N_Def the same as N?

Every FISON contains only a finite set of numbers. ℕ is more.
> 
>> We call that phenomenon potential infinity.
> 
> WHich is just infinity,

Cantor denies your claim.
"Nevertheless the transfinite cannot be considered a subsection of what 
is usually called 'potentially infinite'. Because the latter is not 
(like every individual transfinite and in general everything due to an 
'idea divina') determined in itself, fixed, and unchangeable, but a 
finite in the process of change, having in each of its current states a 
finite size; like, for instance, the temporal duration since the 
beginning of the world, which, when measured in some time-unit, for 
instance a year, is finite in every moment, but always growing beyond 
all finite limits, without ever becoming really infinitely large." [G. 
Cantor, letter to I. Jeiler (13 Oct 1895)]
Here he is right.

Regards, WM