Re: Replacement of Cardinality

On 8/17/2024 7:17 AM, Richard Damon wrote:

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.

Yup. It sure seems as if when he hears something akin to "all the natural numbers", WM's mind thinks FINITE! Wow. Shit happens for sure... ;^)