Re: Replacement of Cardinality

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)  >
...

It seems likely that you're using
an unreliable quantifier shift

>
In case you have no arguments
claim quantifier shift.
Please elaborate.

You do not disclose why you think that
the equation which proves you are wrong
proves that you are right.
"Quantifier shift" is my best guess at
your undisclosed thinking:
⎛ ∀ᴿx > 0: ∃S ⊆ ⅟ℕ: S ᵉᵃᶜʰ< x ∧ |S| = ℵ₀
⎜ 🖙 SHIFT 🖘
⎝ ∃S ⊆ ⅟ℕ: ∀ᴿx > 0: S ᵉᵃᶜʰ< x ∧ |S| = ℵ₀
And hypothetical shifted.S holds your darkᵂᴹ numbers.
Tell me I haven't read your mind!
I've never claimed to be psychic.
But then tell me what you ARE thinking, instead.

(which doesn't become reliable by staying implicit),
but
you (WM) find silence with regard to
the rest of your argument
more advantageous, apparently.

>
There is no rest.

Then there is no argument.
Think about it, before you admit that.
I'd like to address your _best_ argument.
Can you come up with even bad reasons
for shifted.S to exist?