Re: Replacement of Cardinality

Am 07.08.2024 um 23:29 schrieb Jim Burns:

On 8/7/2024 3:01 PM, WM wrote:

Le 07/08/2024 à 20:29, Jim Burns a écrit :

 

The only part of your argument which you've shared is
∀n ∈ ℕ: 1/n - 1/(n+1) > 0

>
That is the decisive part.

Actually, his "thinking process" is simple:
"Since there is a gap (space) between adjacent unit fractions and all unit fractions are in the interval (0, 1], there must be FINITELY MANY of them (i.e. a first/smallest one)." (Don't ask! At least this "argument" seems to be CLEAR FOR HIM).
And of course, in this case:

Never two or more unit fractions are added to NUF [starting with NUF(0) = 0].

Right. And if x1 e IR is "the position" of the first/smallest unit fraction, then NUF(x1) = 1.

you (WM) find silence with regard to
the rest of your argument
more advantageous, apparently.

>
There is no rest.

Right!
I mean, it's an OBVIOUS FACT (in Mückenheim's world).