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Subject: Re: Contradiction of bijections as a measure for infinite sets
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From: WM <wolfgang.mueckenheim@tha.de>
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Le 09/04/2024 à 20:27, Jim Burns a écrit :
> On 4/9/2024 8:22 AM, WM wrote:
>> Le 09/04/2024 à 01:54, Jim Burns a écrit :
>>> On 4/8/2024 9:55 AM, WM wrote:
>>>> Le 07/04/2024 à 21:47, Jim Burns a écrit :
> 
>>>>> The successor operation is closed in
>>>>> the natural numbers.
>>>>
>>>> For visible numbers only.
>>>
>>> Visibleᵂᴹ or darkᵂᴹ,
>>> k is a natural number  :⟺
>>> k=0 ∨ ∃⟦0,k⦆: ∀i ∈ ⟦0,k⦆: i⁺¹ ∈ ⦅0,k⟧
>>
>> Not correct if
>> there are all natural numbers such that
>> no further one exists below ω.
> 
> You seem to be saying:
> | Not correct if
> | not all natural numbers have
> | a further one below ω

All further numbers are multiplied too.
> 
> In other words [1]:
> | Not correct if
> | ω is finiteⁿᵒᵗᐧᵂᴹ.

Not correct if there is no free space between ℕ and ω.

Regards, WM