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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Simple enough for every reader?
Date: Sat, 14 Jun 2025 13:58:06 +0300
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On 2025-06-13 13:45:20 +0000, WM said:

> On 13.06.2025 11:53, Mikko wrote:
>> On 2025-06-12 09:41:51 +0000, WM said:
>> 
>>> On 12.06.2025 09:56, Mikko wrote:
>>>> On 2025-06-11 11:30:26 +0000, WM said:
>>> 
>>>>> For all natural numbers that can be chosen as individuals:
>>>>> |ℕ \ {1, 2, 3, ..., n}| = ℵo.
>>>>> The "..." can be removed by the inductive proof
>>>>> for all definable n ∈ ℕ:
>>>>> |ℕ \ {1}| = ℵo.
>>>>> |ℕ \ {m ∈ ℕ | m < n}| = ℵo
>>>>> ==> |ℕ \ {m ∈ ℕ | m < n+1}| = ℵo.
>>>> 
>>>> That the set difference of an infinite set and a finite set is infinite
>>>> is well understood and therefore an uninteresting result.
>>> 
>>> That is not the only result.
>> 
>> That is the result of your proof. Other results can be discussed in
>> other contexts.
> 
> The following result cannot be circumvented: After mankind will have ceased,

who will care?

> there is a largest natural number ever named.

That has no mathematical significance. Whther a number is nambed or not
is a featurem of mankind, not of the number.

-- 
Mikko