Re: Replacement of Cardinality

On 8/8/2024 4:20 AM, WM wrote:

Le 07/08/2024 à 23:29, Jim Burns a écrit :

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.
Never two or more unit fractions are added to NUF.

>
Arithmetic says:
⅟n  >
⅟(n+1)  >
⅟(n+2)  >
⅟(n+3)  >
⅟(n+4)  >
...

>
NUF(0) = 0.
Never more than one unit fraction can be
added simultaneously to NUF(x).
==> Exists x with x = INVNUF(1).

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

There are two contradicting arguments.
One of them must be wrong.
Or actual infinity is wrong.

⎛ A finite order is trichotomous and
⎜ each non.{} subset with min and max
⎜
⎜ An infinite order is trichotomous and
⎜ has one or more non.{} subsets without min or max.
⎜
⎝ No set has both a finite and an infinite order.
A subset of a set with a finite order
  has only non.{} subsets with min and max
has a finite order.
A superset of a set with an infinite order
  has a non.{} subset without min or max
has an infinite order.
An actuallyᵂᴹ infinite set
( a finite.ordered set with an infinite.ordered subset
does not exist.