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Subject: Re: Replacement of Cardinality
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From: WM <wolfgang.mueckenheim@tha.de>
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Le 21/08/2024 à 20:20, Jim Burns a écrit :
> On 8/21/2024 6:43 AM, WM wrote:
>> Le 20/08/2024 à 22:05, Jim Burns a écrit :
> 
>>> No min.⅟ℕᵈᵉᶠ exists.
>>
>> The reason is potential infinity.
> 
> Is potentialᵂᴹ.infinity mathematicsᵂᴹ?

All of classical mathematics is embedded into potential infinity.
> 
> Judging from your edicts on this topic,
> the answer looks to be both 'yes' and 'no'.

I am interested in actual infinity. We cannot prove its existence but only 
apply logic like this: If a complete chain exists which does not continue 
into the negative, then it ends before. Either at one or at more members. 
The latter is excluded by ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 . 
> 
> 
> We are agreed, though, that
> no min.⅟ℕᵈᵉᶠ exists.

Of course. After each one there will appear more. Choose the smallest one 
you can, recognize that there are many more following.
> 
> It follows that ⅟ℕᵈᵉᶠ has properties that
> the unit.fractionsᵈᵉᶠ > x > 0
> don't have.

There is no set ℕᵈᵉᶠ because of lacking completeness. Sets of set 
theory are complete.

Regards, WM