Re: More complex numbers than reals?

On 7/17/2024 1:57 PM, WM wrote:

Le 17/07/2024 à 19:11, Jim Burns a écrit :

On 7/16/2024 3:33 PM, WM wrote:

What about the infinitely many numbers
which are remainimg from E(1)?

>
None of them remain in
all.infiniteⁿᵒᵗᐧᵂᴹ (all) end segments.

>
What remains to keep the endsegments infinite?

| For each number, there is a number after
  proves false
| There is a number after all numbers.

An infiniteⁿᵒᵗᐧᵂᴹ end segment
common to all infiniteⁿᵒᵗᐧᵂᴹ end segments
not.exists.

>
Because of inclusion monotony
this is a wrong result.

You (WM) aren't referring to ℕⁿᵒᵗᐧᵂᴹ
⎛ Each j in ℕⁿᵒᵗᐧᵂᴹ has in ℕⁿᵒᵗᐧᵂᴹ
⎜ non.0 j⁺¹ immediately.after j
⎜
⎜ Each non.0 k in ℕⁿᵒᵗᐧᵂᴹ has in ℕⁿᵒᵗᐧᵂᴹ
⎜ k⁻¹ immediately.before k
⎜
⎜ Each nonempty subset B ⊆ ℕⁿᵒᵗᐧᵂᴹ holds
⎝ min.B smallest in B.