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Subject: Re: Replacement of Cardinality
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From: WM <wolfgang.mueckenheim@tha.de>
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Le 03/08/2024 à 21:54, Jim Burns a écrit :
> On 8/3/2024 10:23 AM, WM wrote:

>> I recognized lately that you use
>> the wrong definition of NUF.
>>
>> Here is the correct definition:
>> There exist NUF(x) unit fractions u, such that
>> for all y >= x: u < y.

> Here is an equivalent definition:
> There exist NUF(x) unit fractions u, such that
> u < x
> 
>> Note that the order is ∃ u ∀ y.
> 
> The order is ∀x ∃u ∀y
> ∃u ∀x ∀y is an unreliable quantifier shift.

It is not a shift but it is the definition of NUF. It excludes that ∃u 
∀x>0: u < x,

Regards, WM