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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Simple enough for every reader?
Date: Tue, 10 Jun 2025 19:06:18 +0200
Organization: A noiseless patient Spider
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On 08.06.2025 07:10, Mikko wrote:
> On 2025-06-06 10:47:33 +0000, WM said:
> 
>> On 06.06.2025 09:37, Mikko wrote:
>>> On 2025-06-05 20:36:45 +0000, WM said:
>>>
>>>> On 05.06.2025 09:32, Mikko wrote:
>>>>> On 2025-06-04 17:32:28 +0000, WM said:
>>
>>>>> The expression "subtracting them individually" should be represented
>>>>> mathematically, e.g. a sequence. Informal expressions tend to lead
>>>>> to bad proofs.
>>>>
>>>> This expression is represented by
>>>>
>>>> ((((ℕ \ {1}) \ {2}) \ {3}) ...) = { }
>>>
>>> That may be good enough when you want to prove something that we already
>>> believe anyway. But for a sufficiently rigorous proof of something else
>>> the "..." should be replaced with something more mathematicsl.
>>
>> The "..." can be replaced with the singletons of definable natural 
>> numbers
> 
> Then do so.

See above. Three are already given. More can be inserted. But it is 
impossible to replace them with all natural numbers.

Regards, WM