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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 16:15:06 +0200
Organization: A noiseless patient Spider
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In-Reply-To: <101hevt$22j02$1@dont-email.me>

On 01.06.2025 13:53, Mikko wrote:
> On 2025-05-31 13:40:12 +0000, WM said:
> 
>> On 31.05.2025 11:59, Mikko wrote:
>>> On 2025-05-30 14:25:22 +0000, WM said:
>>
>>>> Here I use induction in Cantor's set. That is allowed. Cantor did it 
>>>> too.
>>>
>>> No, there is no artithmetic induction and no set induction there.
>>
>> "daß die Reihe
>>             1, i2, i3, ..., i, ...
>> nur eine Permutation der Reihe
>>             1, 2, 3, ..., , ...
>> ist. Dies beweisen wir durch vollständige Induktion,"
>> [Cantor, collected works, p. 305]
> 
> Did Cantor acurally prove that with a complete induction? As far as
> I have seen Cantor has proven what he promised to prove.

Cantor often used induction: vollständige Induktion. But that is 
irrelevant. It only shows that your claims forbidding the use of 
induction in ℕ are void.

Regards, WM