Re: Replacement of Cardinality

Richard Damon formulated on Saturday :

On 8/17/24 9:30 AM, WM wrote:

Le 16/08/2024 à 19:54, Jim Burns a écrit :

On 8/16/2024 1:00 PM, WM wrote:

 

Start from x = 0.
The increase cannot be more than 1.
∀n ∈ ℕ: 1/n - 1/(n+1) > 0

>
Start from x = 0
The increase cannot be less than 2

 That violates ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 .
 

∀ᴿx > 0:  x  >  ⅟nₓ  >  ⅟(nₓ+1)
nₓ = ⌊1+⅟x⌋

 That holds only for definable numbers.
 Regards, WM
 

>
Which is all of the Rational Numbers, and thus all of the unit fractions.
>
Thats your problem, you don't seem to know how to definie numbers.

Worse than that, he tries to make a set of undefined/undefinable numbers which he calls dark numbers while sets have well defined elements.