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From: WM <wolfgang.mueckenheim@tha.de>
Newsgroups: sci.logic
Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (extra-ordinary)
Date: Sun, 24 Nov 2024 20:42:17 +0100
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On 24.11.2024 20:26, Jim Burns wrote:
> On 11/24/2024 9:05 AM, WM wrote:
>> On 23.11.2024 23:10, Jim Burns wrote:
>>> On 11/23/2024 4:39 PM, WM wrote:
>>>> On 23.11.2024 22:20, Jim Burns wrote:
> 
>>>>> Do you (WM) object to
>>>>>   k ↦ k+1 : one.to.one
>>>>
>>>> I don't know what that waffle should mean.
>>>
>>> k ↦ k+1  means the successor operation.
>>>
>>> 'One.to.one' means that,
>>> if j≠k  then j+1≠k+1
>>> different numbers have different successors.
>>>
>>> I am claiming that
>>> different numbers have different successors.
>>
>> Ok.
> 
> "Ok, I understand you"
>   or
> "Ok, different numbers have different successors"
>   ?

Yes.

> What we mean by
>   |E(k)| ≤ |E(k+1)|
> is that
> there is a one.to.one function
>   from E(k) to E(k+1)
> The successor operation, for example.

What I mean is the fact that
∀k ∈ ℕ: |E(k+1)| = |E(k)| - 1
whereas Cantor's ℵo is a very unsharp measure.
> 
> So, there is.
> So, |E(k)| ≤ |E(k+1)|  isn't wrong.

Cantor's nonsense has many faces. It i not suitable for serious maths.

Regards, WM