Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 10/28/24 5:49 AM, WM wrote:

On 27.10.2024 20:01, FromTheRafters wrote:

WM pretended :

Am 27.10.2024 um 14:39 schrieb FromTheRafters:
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If 'not defined' could be a proper subset of the naturals, then there would be a first such 'not defined' in that subset. Of course WM can't substantiate any of his wild claims.

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Proof:

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Blah blah blah.

 Very substantial.
 Proof: If infinity is actual, then all elements of the set of unit fractions exist. The function NUF(x) = Number of Unit Fractions between 0 and x starts with 0 at 0. After NUF(x') = 1 it cannot change to NUF(x'') =  2 without pausing for an interval consisting of uncountably many real points. The reason is this: ∀n ∈ ℕ: 1/n - 1/(n+1) > 0. Of course x' and x'' are dark rational numbers, the smallest unit fractions.
 Regards, WM
 

Your proof fails because it assumes properties that are not actually required.
If you really mean that there must be a lowest unit fraction, then you system can not have ANY infinity, not even the Natural Numbers, as they DO go on forever, with no highest element, so their recipricals have no lowest element.
Once we note that you system fails to have infinity, it becomes clear that you claims are just your lies that you know something about how mathematics works.
Sorry, but them are the facts.