Re: Replacement of Cardinality

On 8/15/2024 8:43 AM, Moebius wrote:

Am 13.08.2024 um 19:02 schrieb Jim Burns:

INVNUF(1) > ⅟ ⌊⅟INVNUF(1) +1⌋ > ⅟ ⌊⅟INVNUF(1) +2⌋

>
How is INVNUF defined?
(Since you are using it too,
you should know its definition, right?)

When I first saw WM use 'INVNUF'
he said something that meant
INVNUF(n) = _first_ x with NUF(x) = n
When I use INVNUF(n) I only assume that
INVNUF(n) = x with NUF(x) = n
That's why I use ⌊x⌋ = floor(x)
'Any x' still falls within WM's definition and,
in our little whack.a.mole game,
whacks more moles.
Elsethread: <WM>

The first point with unit fractions is x = INVNUF(1).

</WM>
Date: Thu, 15 Aug 24 13:55:13 +0000

WM is now referring to INVNUF in dsm:
He claims that INVNUF(1) and INVNUF(2)
are two different unit fractions.
>
Can you second that claim?

Do you think I might second it,
when I've just proved INVNUF(1) not.exists?
You asked about a definition.
A definition isn't a claim something exists.
A definition is a claim how a word is used.
( p/q = √2 in lowest terms
is not
a claim that √2 is rational.
It is part of proving √2 is irrational.
It, with the proof, is a nonexistence claim for p/q