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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Simple enough for every reader?
Date: Sun, 1 Jun 2025 16:09:23 +0200
Organization: A noiseless patient Spider
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On 01.06.2025 13:58, Mikko wrote:
> On 2025-05-31 13:47:51 +0000, WM said:
> 
>> On 31.05.2025 12:11, Mikko wrote:
>>> On 2025-05-30 14:46:55 +0000, WM said:
>>>
>>
>>>>>> {1, 2, 3, ..., n, n+1} has infinitely many (ℵo) successors is a 
>>>>>> consequence of {1, 2, 3, ..., n} has infinitely many (ℵo) 
>>>>>> successors, and ℵo - 1 = ℵo.
>>>>>
>>>>> Still no proof.
>>>>
>>>> Proof that every definable natural number has more successors than 
>>>> predecessors.
>>>
>>> You have not shown that proof, either.
>>
>> I have above. You cannot understand it. That is a different thing.
> 
> No proof of anything above. Besides, nothing that requires any
> understanding beyond ordinary proof checking cannot be a proof.

There is no further understanding required.
Every definable natural number n has a finite number, n - 1, of 
predecessors and an infinite number, ℵo, of successors, that is more 
than predecessors.

Regards, WM